Security officers inquire a man at a check point and divert traffic at the edge of the security perimeter put into place a distance from the Westgate Shopping Centre in Nairobi, during the stand off operation between Kenyan security forces and gunmen inside the building September 24, 2013. [Photo/Agencies]

NAIROBI - Kenya's president said his forces had "defeated" Islamists from Somalia's al Shabaab on Tuesday, shooting dead five and capturing 11 others suspected of killing 67 people during a four-day siege at a shopping mall.

"The operation is now over," Uhuru Kenyatta told Kenyans in a televised address, adding that more bodies, seemingly both gunmen and hostages, remained under rubble after three floors in part of the Westgate centre collapsed late in the mission.

"We have ashamed and defeated our attackers," he said.

Police said those who stormed into restaurants and shops at a busy lunchtime on Saturday, spraying bullets and grenades, were now either dead or in custody: "Now it is for the forensic and criminal experts," said a police spokesman, Masoud Mwinyi.

The Red Cross said earlier on Tuesday that 63 people were unaccounted for. About 60 civilians were already confirmed dead in the first days of violence. Kenyan officials declined to say late on Tuesday how many more may have died later, with gunmen who had vowed to kill hostages and go down fighting if attacked.

It also remained unclear who the attackers were, beyond their loyalty to al Qaeda-linked al Shabaab, which had demanded Kenya pull troops out of Somalia. The president said he could not confirm they included two or three Americans or a British woman who might be the widow of a London suicide bomber.

However, al Shabaab themselves, on Twitter, denied that any women took part. After days of trumpeting defiance on behalf of those holding out in the mall, however, the group's silence on their fate late on Tuesday suggested their mission had ended.

"There are several bodies trapped in the rubble, including the terrorists," Kenyatta said. He put the confirmed death toll so far at 61 civilians and six security personnel, as well as five of the militants. The official toll previously stood at 62.

Officials said the gunmen had set a major fire on Monday in a supermarket. On Tuesday, a thin trail of smoke drifted into a soggy sky as darkness fell, the result, rescue volunteers said, of soldiers detonating locked doors in a search for militants.

Police were letting some people retrieve cars left behind when shoppers fled in panic as gunmen, whom officials had said numbered about a dozen or more, burst upon them. But journalists and others were still kept well away behind a security cordon.