He said the three-day-long siege by Islamist gunmen, which has left at least 62 dead and up to 200 wounded, was nearing the end.
"Our special forces are inside the building checking the rooms. Obviously it's a very, very big building," said government spokesman Manoah Esipisu.
"We think that everyone, the hostages, have been evacuated, but we don't want to take any chances," he said. "The special forces are doing their job and yes, I think we are near the end."
"The special forces call this sanitising. It's a very complex and very delicate operation," he said, but said no resistance was being encountered.
"At the moment they have not met any resistance, but of course we are not ruling out the possibility that there are a couple of them hiding in a remote room or corner," he told AFP.
Earlier on Monday, four thunderous explosions rattled Nairobi's upscale mall, part of a battle between Kenyan troops and al Qaeda-linked terrorists. Top Kenyan officials said two hostage takers, part of "a multinational collection from all over the world," had been killed.
Kenya's interior minister said the evacuation of hostages went "very, very well".
Kenya chief of defense forces Gen Julius Karangi had said fighters from an array of nations participated in the attack claimed by al Shabab, a Somali group allied with al Qaeda.
"We have an idea who these people are and they are clearly a multinational collection from all over the world," he said.
Timeline: al Shabab attacks in Somalia, other nations
Earlier, Kenya's interior minister Joseph Ole Lenku also revised the death toll to 62, seven lower than previously reported.
Kenyan officials had said 59 people have died since the siege on Westgate Mall began on Saturday, while the Red Cross had put the toll at 68, then in a tweet lowered it to 62, saying some bodies had been counted twice.
Dark plumes of smoke rose from the mall for more than an hour after four large explosions rocked the upscale Westlands neighborhood.
A plume of black smoke billows over the Westgate Mall, following large explosions and heavy gunfire, in Nairobi. (AP Photo)
A person with knowledge of the rescue operation earlier told The Associated Press that the smoke was rising up and out of a large skylight inside the mall's main department and grocery store, Nakumatt, where goods like mattresses may have been lit on fire.
General Karangi said Kenyan forces were in charge of all floors inside the mall, though terrorists could still be hiding inside.
Earlier witness reports had indicated that a woman was among the estimated 10 to 15 attackers. Lenku said that instead some male attackers had dressed up like women.
Read: Security footage shows how gunmen stormed Nairobi mall: report
The four explosions were followed by volleys of gunfire, then a thick, dark column of smoke that burned for roughly 90 minutes. Military and police helicopters and one plane circled over the Nairobi mall, giving the upscale neighborhood the feel of a war zone.
Kenya Security personnel take cover outside the Westgate Mall after firing started inside the mall. (AP Photo)
On Sunday Kenyan officials announced that "most" hostages had been rescued. But no numbers were given. Kenyan officials have never said how many hostages they thought the attackers had, but have said preserving the hostages' lives was a top priority, greatly complicating the final fight against the attackers.
From neighboring Somalia, spokesman Sheik Ali Mohamud Rage for al Shabab - the militant group that claimed responsibility for the attack - said in an audio file posted on a website that the hostage takers had been ordered to "take punitive action against the hostages" if force was used to try to rescue them.
At the Oshwal Centre next to the mall, the Red Cross was using a squat concrete structure that houses a Hindu temple as a triage center. Medical workers attended to at least two wounded Kenyan soldiers there on Monday.
Al- Shabab said on a Twitter feed, an account that unlike some others appears to be genuine, that the attackers had lots of ammunition. The feed said that Kenya's government would be responsible for any loss of hostages' lives.
Read: Shabab Twitter account suspended after attack claims
A large military assault began on the mall shortly before sundown on Sunday, with one helicopter skimming very close to the roof of the shopping complex as a loud explosion rang out, far larger than any previous grenade blast or gunfire volley. Officials said the siege would soon end and said "most" hostages had been rescued and that officials controlled "most" of the mall. But on Monday the standoff remained.
Kenyan cabinet secretary for interior and coordination of national government Joseph ole Lenku gives a press conference outside the part Israeli-owned Westgate mall. (AFP Photo)
As the crisis surpassed the 48-hour mark, video taken by someone inside the mall's main department store when the assault began emerged. The video showed frightened and unsure shoppers crouching as long and loud volleys of gunfire could be heard.
Read: Victims of the Kenya mall attack
The al Shabab extremists stormed the mall on Saturday from two sides, throwing grenades and firing on civilians.
Kenyan authorities said they would do their utmost to save hostages' lives, but no officials could say precisely how many people were being held captive.
Kenya's Red Cross said in a statement, citing police, that 49 people had been reported missing. Officials did not make an explicit link but that number could give an indication of the number of people held captive.
Kenya security personnel take cover outside the Westgate Mall after shooting started inside the mall. (AP Photo)
Al Shabab said the attack, targeting non-Muslims, was in retribution for Kenyan forces' 2011 push into neighboring Somalia.
"If you want Kenya in peace, it will not happen as long as your boys are in our lands," Rage said.
The group also issued a string of statements via Twitter, one of them claiming that Muslims in the centre had been "escorted out by the Mujahideen before beginning the attack".
Read: UN leader Ban Ki-moon condemns Kenya mall attack
Early developments on Monday
As the stand-off entered its third day, sustained bursts of rapid gunfire broke out at dawn, and soldiers posted around the complex ducked for cover. This was followed by three big explosions and more sporadic weapons fire, AFP correspondents at the scene said.
The Kenyan army said it had secured most of the upmarket, part Israeli-owned complex, while a security source said a final assault was underway against the al Qaeda-linked Somali Shabab rebels, believed to be pinned down in a part of the mall but using hostages as human shields.
"Our concern is to rescue all hostages alive and that is why the operation is delicate," the Kenya Defence Forces said in a statement overnight, adding that it was trying to bring a "speedy conclusion" to the drama.
Medics take cover as gunfire and explosions are heard from Nairobi's Westgate Mall. (AP Photo)
It did not say how many people were being held by the dozen-or-so attackers, who marched into the sprawling four-storey complex at midday Saturday, spraying shoppers with machine gun fire and tossing grenades.
In an address to the nation on Sunday, Kenyan President Uhuru Kenyatta had vowed the attackers will "not get away with their despicable and beastly acts."
A Kenyan security source and a Western intelligence official added Israeli forces were involved in the operation, along with British and US agents.
Read: US promises support to Kenya to bring attackers to justice
Indians killed, injured
Two Indians, including an 8-year-old boy, were among 43 killed and four other Indian nationals injured in the attack by armed terrorists in the mall.
While one of the victims 40-year-old Sridhar Natarajan was working with a pharma firm, the boy Paramshu Jain was the son of a manager of the local Bank of Baroda branch, Syed Akbaruddin, spokesperson in the ministry of external affairs (Government of India) said.
Four Indians, including two women and a girl, were injured in the attack and are receiving medical treatment, the spokesperson said.
India's mission in Nairboi is in touch with the families of the deceased, the spokesperson said.
Volunteers from the asian-community run for cover after hearing a volley of gunshots. (AFP Photo)
Read: PM Manmohan Singh condemns Nairobi terror attack
Syed Akbaruddin tweeted: "Update on Nairobi attack: 4 Indians including 2 women, male adult and girl injured. Two others - employee of pharma firm and a boy sadly died."
@AkbarMEA tweeted: "Indians injured in Nairobi attack: Smt Manjula Sridhar; Smt Mukta Jain; Kumari Poorvi Jain; Shri Natarajan Ramachandran."
"#India's Mission in Nairobi in touch with families of - Sridhar Natarajan 40 years and Paramshu Jain, 8 years who tragically died in attack," he also tweeted.
Gujarat chief minister Narendra Modi also on Sunday expressed his condolences for the people who died in the 'terrorist' attack in Kenya and said that "the time has come to take steps to wipe out terrorism from the world."
Exclusive: Indian living 2 minutes away from Westgate Mall speaks to HT
Bodies still in mall unaccounted for
Terrified witnesses told of scenes of horror and panic as the masked gunmen stormed in. Officials estimated some 200 people have been wounded, and the Red Cross made a nationwide appeal for blood donors.
Police sources who had entered the building on Sunday evening said they feared that death toll "could be much, much higher... judging from the bodies sighted inside."
A number of witnesses have been quoted as saying that the gunmen were trying to weed out non-Muslims for execution by interrogating people on their faith or asking them to say the Shahada, or Islamic creed.
The dead included three Britons, two French women, two Canadians including a diplomat, a Chinese woman, two Indians, a South Korean, a South African and a Dutch woman, according to their governments. The UK Foreign Office said on Monday it had confirmed the deaths of four British nationals. Also killed was Ghanaian poet and former UN envoy Kofi Awoonor, 78, while his son was injured.
A man rescued by Kenyan troops at the Westgate Mall. (AFP Photo)
'People sprayed with bullets'
In the hours after the attack began, shocked people of all ages and races could be seen running from the mall, some clutching babies, while others crawled along walls to avoid stray bullets.
Mall worker Zipporah Wanjiru, who emerged from the ordeal alive but in a state of shock, said she hid under a table with five other colleagues.
"They were shooting indiscriminately, it was like a movie seeing people sprayed with bullets like that," she said, bursting into tears.
Security camera footage seen by Kenya's The Standard newspaper shows gunmen raking toilet cubicles with a barrage of gunfire, apparently after learning that several people were hidden inside.
Fighters later holed up in a cinema on the top floor and a security room of a supermarket, it added.
Cafe waiter Titus Alede, who risked his life and leapt from the first floor of the mall, said it was a "miracle from God" that he managed to escape the approaching gunmen.
"I remember them saying 'you killed our people in Somalia, it is our time to pay you back'," he said.
Other survivors said they played dead to avoid being killed.
Read: Teenager 'played dead' to survive attack
Kenyan president says nephew killed
Kenyan President Uhuru Kenyatta said on Sunday a nephew and his fiancee were among the 68 people confirmed killed in an ongoing siege in an upmarket shopping mall by Somali militants.
"I feel the pain of every life we have lost, and share your grief at our nation's loss," Kenyatta said, calling his killed relatives "young, lovely people I personally knew and loved."
"They shall not get away with their despicable and beastly acts," Kenyatta said in an emotional speech to the nation.
"We will punish the masterminds swiftly and indeed very painfully."
Al Shabab behind attack
Al Shabab, on its Twitter feed, said that it has many times warned Kenya's government that failure to remove its forces from Somalia "would have severe consequences." The group claimed that its gunmen had killed 100 people, but its assertions are often exaggerated.
"The attack at #WestgateMall is just a very tiny fraction of what Muslims in Somalia experience at the hands of Kenyan invaders," al-Shabab said.
Another tweet said: "For long we have waged war against the Kenyans in our land, now it's time to shift the battleground and take the war to their land #Westgate."
File photo of members of Somalia's al Shabab jihadist movement, seen during exercises at their military training camp outside Mogadishu. (AP Photo/File)
Al Shabab's Twitter account was suspended shortly after its claim of responsibility and threats against Kenya. Twitter's terms of service forbids making threats.
Al Shabab threatened in late 2011 to unleash a large-scale attack in Nairobi. Kenya has seen a regular spate of grenade attacks since then but never such a large terrorist assault.
The gunmen told hostages that non-Muslims would be targeted, said Elijah Kamau, who was at the mall at the time of the midday attack.
"The gunmen told Muslims to stand up and leave. They were safe, and non-Muslims would be targeted," he said.
Jay Patel, who sought cover on an upper floor in the mall when shooting began, said that when he looked out of a window onto the upper parking deck of the mall he saw the gunmen with a group of people. Patel said that as the attackers were talking, some of the people stood up and left and the others were shot.
The attack was carried out by terrorists, said police chief Benson Kibue. He did not specify a group. He said it was likely that no more than 10 attackers were involved.
Somalia's president - the leader of a neighboring country familiar with terrorist attacks - said his nation knows "only too well the human costs of violence like this" as he extended prayers to those in Kenya.
"These heartless acts against defenseless civilians, including innocent children, are beyond the pale and cannot be tolerated. We stand shoulder to shoulder with Kenya in its time of grief for these lives lost and the many injured," President Hassan Sheikh Mohamud said.
The gunmen carried AK-47s and wore vests with hand grenades on them, said Manish Turohit, 18, who hid in a parking garage for two hours.
"They just came in and threw a grenade. We were running and they opened fire. They were shouting and firing," he said after marching out of the mall in a line of 15 people who all held their hands in the air.
Rumours swirled that non-Somalis were among the fighters, but the Shabab said they had released no information about the identies of any of the insurgents.
People donate blood for those injured persons in the attack on Nairobi's Westgate Mall. (AP Photo)
The build up
Israeli interests in Kenya have come under attack before, and the Westgate mall has long been seen as a potential target.
World powers condemned the attack, which is the worst in Nairobi since an al Qaeda bombing at the US embassy killed more than 200 people in 1998.
US President Barack Obama called Kenyatta offering support "to bring the perpetrators of the attack to justice", while UN chief Ban Ki-moon said the violence was "totally reprehensible".
(With AFP and AP and Reuters inputs)