completed," a sombre Kenyatta, who himself lost family members in the assault, said in a televised address to the nation.
The president said "three floors of the mall collapsed, trapping several bodies within the rubble including those of terrorists."
Police said the current death toll was provisional, while the Kenyan Red Cross said 63 people were still listed as missing.
"Our losses are immense," the president said, announcing three days of national mourning.
Five attackers had been killed and 11 suspects were in custody. Somalia's al Qaeda-linked Shabab rebels said the group carried out the attack in retaliation for Kenya's military intervention in the country.
"We have been badly hurt, but we have been brave, united and strong. Kenya has stared down evil and triumphed. We have defeated our enemies and showed the whole world what we can accomplish," he said.
In one of the worst attacks in the country's history, a group of attackers marched into the four-storey, part Israeli-owned Westgate Mall at midday Saturday, spraying shoppers with automatic weapons fire and tossing grenades.
Somalia's al Qaeda-linked Shebab rebels said they carried out the attack in retaliation for Kenya's two-year battle against the extremists' bases in the country. "It's an eye for an eye and a tooth for a tooth," the group said on Twitter late on Tuesday night.
Kenyatta said that "forensic investigations are under way to establish the nationalities of all those involved" amid reports Americans and a British woman were among the insurgents.
Highlights from his address:
• 'Losses immense' from mall attack: Kenyan President
• 'We have ashamed and defeated our attackers': Kenyan president
• Kenya president declares three days of national mourning
• Terrorists defeated, 3 mall floors collapsed: Kenyan president
• Five mall attackers killed, 11 suspects arrested: Kenyan president
• 61 civilians including 6 security forces killed in mall attack, more bodies trapped: Kenyan president
There has been growing media speculation at the possible role of wanted British extremist Samantha Lewthwaite, daughter of a British soldier and widow of suicide bomber Germaine Lindsay, who blew himself up on a London Underground train on July 7, 2005, killing 26 people.
The president said intelligence reports had suggested that a British woman and two or three American citizens "may have been involved in the attack", but that could not yet be confirmed.
Lewthwaite is wanted in Kenya, and is accused of links to the Shabab -- although the rebels later "categorically" denied the involvement of any woman in the attack, insisting they had "an adequate number of young men who are fully committed".
Shabab spokesman Ali Mohamud Rage also threatened further "black days" if Kenya did not bring troops home, warning the siege was just "a taste of what we will do".
For his part, Kenyatta vowed "full accountability for the mindless destruction, deaths, pain, loss and suffering we have all undergone."
"These cowards will meet justice, as will their accomplices and patrons, wherever they are."
Close to 200 were wounded in the four-day long carnage, which saw running battles between militants and security forces in the complex, Nairobi's largest shopping centre and popular with wealthy Kenyans, diplomats, UN workers and other expatriates.
The siege developed into a hostage drama with Shabab claiming civilians were being held, and Kenyan special forces describing the stand-off as delicate -- with gunman running and hiding in supermarket aisles, store rooms, a cinema and casino and placing booby traps.
Officials and intelligence sources said they were backed by Israeli, US and British agents.
Non-Muslims selected for execution
Shocked witnesses said the attackers weeded out non-Muslims for execution by demanding they recite the Shahada, the Muslim profession of faith.
"When I mentioned the first word of the Shahada (creed), they moved on. That is how I survived," one survivor said. Another saw people being questioned, then executed.
Children, some of whom were taking part in a cooking competition hosted by popular radio personalities, were also gunned down. Competition host Ruhila Adatia-Sood, a TV and radio personality who was six months pregnant, was shot dead.
"The kids were just running around in their little aprons, chopping up. We heard a series of gunshots," said Aleem Manji, whose radio station East FM was hosting the party. "We said get down, get down, get down on the floor. And just as we did that, the gunmen tossed a grenade to where we were."
As well as scores of Kenyans - from ordinary workers to the president's nephew - many of the dead were foreigners, including six Britons, two Canadians, a Chinese woman, a Dutch woman, two French women, two Indians, a South African and a South Korean.
Some of the survivors recounted how they hid under cars in the parking area, while others played dead or barricaded themselves inside shops. Security camera footage showed gunmen subjecting toilet doors to a barrage of gunfire, apparently after learning that large numbers of people were holed up inside.
Blood donor appeals ended after banks filled with donations from hundreds, while over $650,000 (490,000 euros) has been raised to support the families affected.
Israeli interests in Kenya have come under attack before, and the Westgate mall - frequented by well-to-do Kenyans, diplomats, UN workers and other expatriates -- has long been seen as a potential target.
The siege, which has revived memories of the 2008 Mumbai attacks, is the worst attack in Nairobi since an al Qaeda bombing at the US embassy killed more than 200 people in 1998.
US President Barack Obama, whose father was Kenyan, has called Kenyatta offering "whatever law enforcement support that is necessary".
Intelligence sources from two foreign countries who could not be named said there had been no leaks or "chatter" ahead of the attack, despite close monitoring of the Shebab's operations. The Westgate mall, however, has long been considered a potential "soft" target for extremists.
Meanwhile, Somalia’s prime minister appealed on Tuesday for international support to combat al Shabaab militants but said a military solution to their insurgency alone was not enough.
Addressing the UN Human Rights Council in Geneva , Abdi Farah Shirdon denounced what he called the “cowardly attack” by al Shabab militants on a shopping mall in the Kenyan capital Nairobi and said those responsible must be held accountable.
He praised the 17,000-strong African peacekeeping force deployed in Somalia for improving security and fighting al Shabab, who he said were now weakened.
But Somalia, emerging from two decades of civil war, still faced many challenges, he said.
“We still have a difficult journey ahead of us. A military solution alone is not enough, promotion of rule of law, greater regional cooperation and economic stability and provision of public services are all key factors that complement the military effort,” Shirdon said in his speech.
A government priority was to cut youth unemployment.
“This provided al Shabab a building ground to recruit and spread their destructive ideology. It is therefore essential to create educational and economic opportunities for youth,” he said.