* Kenyan president says militants "defeated"
* Says 5 militants dead, 11 held, 67 other people dead
* Bodies still under rubble of collapsed floors
* Unclear if security operation completely over
* Unclear if British woman, Americans among militants
By Richard Lough and Edmund Blair
NAIROBI, Sept 24 (Reuters) - Kenya's president said on Tuesday that his forces had "defeated" Islamists from Somalia's al Shabaab, had shot five of them dead and detained 11 others suspected of killing 67 people after storming a Nairobi shopping mall.
It remained unclear after Uhuru Kenyatta addressed the nation on television whether the four-day security operation at the upmarket Westgate centre was completely over, or whether any militants were still at large or hostages unaccounted for.
"We have ashamed and defeated our attackers," Kenyatta said, adding that bodies were still trapped under rubble following the collapse of part of the building late in the operation. A fire began on Monday which officials said was started by the gunmen.
Sixty-one civilians and six security personnel had been confirmed killed in the four days of bloodshed, Kenyatta said. Five of the attackers were shot dead and 11 suspects were in custody: "Kenya has stared down evil and triumphed," he said.
The president added that he could not confirm intelligence reports that a British woman and two or three Americans might be involved. Forensic scientists were involved in trying to identify the nationalities of the "terrorists", he said.
"Towards the tail end of the operation, three floors of the Westgate mall collapsed and there are several bodies trapped in the rubble including the terrorists," he added. The death toll had previously been put by officials at 62.
"These cowards will meet justice as will their accomplices and patrons, wherever they are," said the president, who thanked other leaders for support and used his address to both praise the response of the Kenyan people and call for national unity, six months after his election was marked by ethnic tensions.
Kenyatta had rejected the militants' demands that he pull Kenyan troops out of its northern neighbour. As part of an African peacekeeping force in Somalia, Kenyan forces have pushed al Qaeda-linked al Shabaab on to the defensive over the past two years.
Kenyan officials have announced the imminent end of the siege for the past three days - something al Shabaab spokesmen have mocked in commentaries and in postings on social media.
Some hours before Kenyatta spoke, the group said its militants were still holding out with hostages and that there were "countless dead bodies" still inside the complex.
"There are countless number of dead bodies still scattered inside the mall, and the Mujahideen are still holding their ground #Westgate," the group said on its Twitter feed.
"The hostages who were being held by the Mujahideen inside #Westgate are still alive, looking quite disconcerted but, nevertheless, alive."
It described its fighters as "unruffled and strolling around the mall in such sangfroid manner".
In an audio statement posted via Twitter, al Shabaab spokesman Sheikh Ali Mohamud Rage called the militants' action a "deadly thrust" by "loyal soldiers seeking to rewrite history". If Kenya failed to pull troops out of Somalia and free al Shabaab prisoners it should "expect black days".
The attack has come at a time when several violent Islamist groups from Mali to Algeria, Nigeria to Kenya - tapping into local grievances but all espousing an anti-Western, anti-Christian creed - are striking at state authority and international interests.
Earlier on Tuesday, the Kenyan military said its forces were carrying out "mop up operations" in the building.
The Interior Ministry earlier said security forces were in control of the mall and that all the hostages had been released.
Images from closed-circuit television inside the mall during the attack, published in a Kenyan newspaper on Tuesday, showed two militants, casually dressed and wearing ammunition belts. One held an assault rifle. Al Shabaab confirmed that the two men were part of the group that attacked Westgate.
Kenyan Foreign Minister Amina Mohamed told PBS television in the United States that "two or three Americans" and a British woman were among the militants.
She said the Americans were "young men, about between maybe 18 and 19" years old. She said they were of Somali or Arab origin and had lived in "in Minnesota and one other place".
Al Shabaab, which said it had been in communication with its members in the mall, dismissed the minister's comments.
"Those who describe the attackers as Americans and British are people who do not know what is going on in Westgate building," al Shabaab's media office told Reuters.
A British security source said it was possible that Samantha Lewthwaite, the widow of Germaine Lindsay, one of the suicide bombers who killed more than 50 people on London's transport system in 2005, was involved in the Nairobi siege.
When asked about reports that Lewthwaite, dubbed the "white widow" by the British media, was directly involved in the attack in Kenya, the source said: "It is a possibility. But nothing definitive or conclusive yet."
Lewthwaite is thought to have left Britain several years ago and is wanted in connection with an alleged plot to attack hotels and restaurants in Kenya.
U.S. security sources said they were looking into information from Kenya that residents of Western countries, including the United States, may have been among the militants.
U.S. President Barack Obama, whose father was born in the east African nation, offered help, saying he believed Kenya - the scene of one of al Qaeda's first major attacks, in 1998, and a neighbour of chaotic Somalia - would continue to be a regional pillar of stability.
Somalia's prime minister appealed in Geneva on Tuesday for international support to combat al Shabaab but said a military solution to their insurgency alone was not enough.
Abdi Farah Shirdon 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."
The attack on the mall is the worst such incident in Kenya since al Qaeda killed more than 200 people when it bombed the U.S. 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.
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 Shabaab.
It has also suffered internal instability. President Kenyatta, who lost a nephew in the weekend bloodbath, 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.
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.
Conflicting comments have fuelled speculation about the attackers' identity. While the foreign minister said there was a woman attacker killed, Interior Minister Joseph Ole Lenku had said on Monday they were all men but some had dressed as women.