previous ones were cut off, the the al Qaida-linked rebel group al-Shabab said the attack that began Saturday and has claimed more than 60 lives so far was "far greater than how the Kenyans perceive it."
"There are countless number of dead bodies still scattered inside the mall, and the mujahideen are still holding their ground," the group claimed.
It added that the hostages are "still alive looking quite disconcerted but, nevertheless, alive."
The Kenyan police responded with a Twitter message of its own, urging people to ignore "enemy... propaganda" and assuring that the defense forces were continuing to "neutralize" the terrorist threat.
"Troops now in mop up operations in the building," the police said. "More to follow. Be calm."
Kenyan special forces are still battling "one or two" Islamist militants holed up inside Nairobi's Westgate shopping mall, security sources involved in the operation said.
The sources said the militants were located and isolated in or around a casino located on one of the upper floors of the complex.
Kenya's Citizen TV reported that troops had killed "six of the remaining attackers" at the mall, but did not give further details and the report was unsourced.
"Security forces killed six of the remaining attackers," the channel said in a brief headline. Officials earlier said three of the 10 to 15 people who stormed the building on Saturday had been killed.
Three Indians were killed in the attack, including an 8-year-old boy, Paramshu Jain, whose father is manager of a Nairobi branch of an Indian bank. The child's mother, Mukta Jain, is among four Indians who were injured.
The others confirmed dead by the Indian external affairs ministry are Sridhar Natarajan, a 40-year-old from India's southern state of Tamil Nadu, and Sudharshan B. Nagaraj, of the southern city of Bangalore.
Earlier on the day, a heavy burst of gunfire was also heard from the mall where at least 62 people were killed, suggesting that the complex had not yet been secured, a Reuters witness said on Tuesday.
Kenya's interior ministry had said early on Tuesday that its forces were "in control" of the mall and had freed all hostages three days after a deadly siege by Islamists, who include "two to three Americans" and a British woman.
He had said that all hostages trapped by the militants are believed to have been freed, Kenyan foreign minister Amina Mohamed underlined the global scope of the attack.
"Our special forces are inside the building checking the rooms. We think that everyone, the hostages, have been evacuated, but we don't want to take any chances," Manoah Esipisu said.
"The special forces call this sanitising. 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 added.
"We're in control of Westgate," the interior ministry said in a message on Twitter. Throughout the night the area around the mall was quiet, with security personnel either moving or appearing relaxed.
The foreign minister, Amina Mohamed, said in an interview with the Public Broadcasting Service's "NewsHour" program that the Americans were 18 to 19 years old, of Somali or Arab origin and lived "in Minnesota and one other place" in the US.
Shabab has claimed responsibility for the attack, which began at lunchtime on Saturday. Kenyan officials say there were 10 to 15 attackers.
It had said on its Twitter feed 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."
Obama, whose father was born in Kenya, said the United States stood with Kenyans against "this terrible outrage".
"We will provide them with whatever law enforcement support that is necessary. And we are confident that Kenya will continue to be a pillar of stability in eastern Africa," he said in New York.
Kenyan security forces believed the end was in sight for the siege at the upmarket shopping mall in the capital, saying its forces were "in control" as the ordeal entered its fourth day.
A government official said there was no resistance from the attackers late on Monday night after a barrage of gunfire and blasts throughout the day, but that the security forces were cautious in case some attackers were hiding in the building.
Read: US promises support to Kenya to bring attackers to justice
"Our forces are combing the mall floor by floor looking for anyone left behind. We believe all hostages have been released," the ministry of interior said on Twitter.
The siege has followed a pattern of bursts of gunfire and activity followed by long lulls.
A plume of black smoke billows over the Westgate Mall, following large explosions and heavy gunfire, in Nairobi. (AP Photo)
Patronised by well-to-do Kenyans and expatriates, Westgate mall epitomised the African consumer bonanza that is drawing foreign investment - from West and East - to one of the world's fastest growing regions. al Qaeda killed more than 200 people when it bombed the US Embassy in Nairobi in 1998. When fighters from its Somali ideological counterpart stormed the mall on Saturday, they hit a high-profile symbol of Kenya's economic power.
Read: Security footage shows how gunmen stormed Nairobi mall: report
Kenya has sent troops to Somalia as part of an African Union force trying to stabilise the country, which was long without a functioning government, and push back al Shabab. It has also suffered internal instability.
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."
Kenya Security personnel take cover outside the Westgate Mall after firing started inside the mall. (AP Photo)
The President faces charges of crimes against humanity at the International Criminal Court for his alleged role in coordinating violence after disputed elections in 2007. He denies the charges.
Kenyatta has dismissed a demand that he pull Kenyan forces out of Somalia, saying he would not relent in a "war on terror".
British defence secretary Philip Hammond said he believed six Britons had died in the attack. Other known foreign victims are from China, Ghana, France, the Netherlands and Canada. Kenyan officials said the total death toll was at least 62.
Read: Al Shabab: who are they, what they want
Kenya believes there are also foreigners among the attackers, with military chief Julius Karangi saying they came from all over the world. "We are fighting global terrorism here," he said, without giving their nationalities.
US authorities are urgently looking into information given by the Kenyan government that residents of Western countries, including the United States, may have been among the attackers, US security sources said.
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)
White House deputy national security adviser Ben Rhodes said he had no direct information that Americans had participated in the attack, but expressed US worries.
"We do monitor very carefully and have for some time been concerned about efforts by al Shabab to recruit Americans or US persons to come to Somalia," Rhodes told reporters travelling with Obama to the United Nations in New York.
Read: Several Americans among attackers: Kenyan official
Interior minister Joseph Ole Lenku said the militants had set fire to mattresses in a supermarket on the mall's lower floors and his ministry later said the blaze was under control.
Two attackers were killed on Monday, taking the total of dead militants so far to three, he told a news conference.
Medics take cover as gunfire and explosions are heard from Nairobi's Westgate Mall. (AP Photo)
Speculation rose about the identity of the attackers. Ole Lenku said they were all men but that some had dressed as women.
Despite his comments, one intelligence officer and two soldiers told Reuters that one of the dead militants was a white woman. This is likely to fuel speculation that she is the wanted widow of one of the suicide bombers who together killed more than 50 people on London's transport system in 2005.
Called the "white widow" by the British press, Samantha Lewthwaite is wanted in connection with an alleged plot to attack hotels and restaurants in Kenya. Asked if the dead woman was Lewthwaite, the intelligence officer said: "We don't know."
Read: Shabab Twitter account suspended after attack claims
A spokesman for al Shabab warned they would kill hostages if Kenyan troops tried to storm their positions. "The mujahideen will kill the hostages if the enemies use force," Sheikh Ali Mohamud Rage said in an online audio statement.
From Mali to Algeria, Nigeria to Kenya, violent Islamist groups - tapping into local poverty, conflict, inequality or exclusion but espousing a similar anti-Western, anti-Christian creed - are striking at state authority and international interests, both economic and political.
John Campbell, a former US ambassador to Nigeria, said he believed insurgents such as those who rebelled in Mali last year, the Nigerian Boko Haram Islamist sect and the Nairobi mall raiders were also partly motivated by anger with what he called "pervasive malgovernance" in Africa.
"This is undoubtedly anti-Western and anti-Christian but it also taps into a lot of deep popular anger against the political economy in which they find themselves, in which a very small group of people are basically raking off the wealth," he said.
Indians killed, injured
Three Indians, including an 8-year-old boy, were among 62 killed and four other Indian nationals injured in the attack by armed terrorists in the mall.
India's mission in Nairboi is in touch with the families of the deceased, the spokesperson said.
Read: Indian shot for failing to answer query on Islam
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."