* Fate of fighters, people listed as missing remains unclear
* Kenya says 2-3 Americans, British woman among militants
* Kenya to remain pillar of east African stability -Obama
* Besieged mall symbol of African economic boom
Kenya said it was in control of a Nairobi shopping mall that was attacked at the weekend but was still searching on Tuesday for Somali-linked Islamists believed to include Americans and a British woman who launched the assault that killed 62 people.
A burst of gunfire in the early morning broke hours of calm on the fourth day since militants of the al Qaeda-aligned al Shabaab group stormed into the Westgate centre during a busy Saturday lunchtime, spraying bullets and tossing grenades.
Helicopters buzzed over the complex that is popular with foreigners and prosperous Kenyans, which al Shabaab said its militants had attacked to demand Kenya withdraw troops from Somalia where they have battled the Islamist group.
President Uhuru Kenyatta has vowed to stay the course there.
"There are still gunmen in the building," said an intelligence officer, who asked not to be named, speaking in the morning near the mall which is surrounded by troops. Asked if there were still hostages, he said: "We are not sure yet."
"We are still in there and going through every room," said one Kenyan soldier.
The Interior Ministry had hours earlier said security forces were searching for anyone left behind in the mall that was now in their control, and that all the hostages had been released.
A trickle of survivors left on Monday, but the fate of those still missing was unclear. It was also unclear how many of the militants had been killed or captured.
The government said on Monday three died and an unsourced television report on Tuesday said "six of the remaining attackers" were killed. There has been no clear official tally.
Foreign Minister Amina Mohamed told the U.S. PBS Newshour television show 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."
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.
"We do monitor very carefully and have for some time been concerned about efforts by al Shabaab to recruit Americans or U.S. persons to come to Somalia," White House deputy national security adviser Ben Rhodes said, adding he had no direct information that Americans participated.
A spokesman for the British High Commission in Nairobi said:
"We are not going to be drawn into speculation about the identity of the attackers while the investigation is ongoing."
Britain, Kenya's former colonial ruler, has like other nations offered support to help pursue those behind the attack.
U.S. President Barack Obama, whose father was born in the east African nation, offered U.S. 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.
Kenyan officials have tried to reassure the country that they are in command of the situation. Officials said there would a news briefing on the situation later on Tuesday.
"We appeal for patience, keep calm, avoid Westgate at all costs and wait for the official communication," the Ministry of Interior and Coordination of National Government in The Office of the President said on Twitter.
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.
'WAR ON TERROR'
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.
Kenyatta has dismissed the demand 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.
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.
A Kenyan intelligence officer and two soldiers also told Reuters that one of the dead militants was a white woman, likely 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."
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 U.S. 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.