Eyewitnesses saw armed men in black, their heads covered in scarves, entering the Westgate shopping centre on Saturday afternoon
An unknown number of hostages are still inside a shopping centre in the Kenyan capital Nairobi after a deadly assault by al-Shabab militants, say officials.
At least 39 people died when members of the Somali Islamist group stormed the Westgate centre on Saturday.
Officials say the gunmen have been cornered but that people are trapped in a number of locations.
Kenyan President Uhuru Kenyatta earlier vowed to "hunt down the perpetrators wherever they run to".
Al-Shabab told the BBC it carried out the attack on the upmarket shopping centre in response to Kenyan military operations in Somalia.
There are about 4,000 Kenyan troops in the south of Somalia, where they have been fighting the militants since 2011.
On its Twitter feed, al-Shabab - which has links to al-Qaeda - said it was behind what it called the "Westgate spectacle".
'Watching and monitoring'
Kenyan officials said "major operations" were under way with police and soldiers preparing an apparent bid to bring an end to the stand-off.
They said the security forces had finally "pinned down" the surviving gunmen.
"The work is continuing, but you cannot rush these things," an army officer posted on the perimeter cordon set up around the mall told the AFP news agency.
"Our teams are there, we are watching and monitoring, we will finish this as soon as we can."
The authorities have asked journalists to exercise caution when reporting military developments because the gunmen might be monitoring the media.
"Hostiles suspected to have access to the internet," the Disaster Operation Centre in Nairobi posted on Twitter.
"Reports on personnel movement and progress will not be posted for fear of compromising strategy."
The officials said the number of hostages was "still unknown, but they are in several locations".
"The gunmen have been contained in one location, but there are hostages elsewhere in the vicinity who cannot access the exit".
Upper levels of the mall had been secured, it said.
The attack began at about 12:00 local time (09:00 GMT), when around the attackers entered the Westgate centre throwing grenades and firing automatic weapons. A children's day event was being held at the time - children are among those reported killed.
Some witnesses said the militants told Muslims to leave and said non-Muslims would be targeted.
"They came and said: 'If you are Muslim, stand up. We've come to rescue you'," said Elijah Lamau.
He said the Muslims left with their hands up, and then the gunmen shot two people.
Scores of people fled or were evacuated while police and armed security guards fought running gun battles with the militants throughout the mall for hours.
As night fell in Nairobi, two contingents of army special forces troops were reported to have moved inside the mall.
The BBC's security correspondent Frank Gardner says a security source told him that at least one of the attackers was a woman who appeared to have some kind of leadership role.
One gunman was arrested and died of his wounds, Kenyan officials told the BBC. Four other gunmen were arrested.
In a televised address on Saturday evening, Mr Kenyatta said security forces were "in the process of neutralising the attackers and securing the mall".
He went on: "We shall hunt down the perpetrators wherever they run to. We shall get to them and we shall punish them for this heinous crime."
He said he had "personally lost family members in the Westgate attack".
Security experts are reported to have long warned that the complex, which is part Israeli-owned, was in danger of being subjected to a terror attack.
The BBC's Mark Doyle, who is embedded with the African Union (AU) mission in Somalia, says the AU troops attack al-Shabab where they can.
Al-Shabab says the AU forces are invaders stopping their legitimate vision of creating an Islamic state and respond by mounting hit-and-run attacks, our correspondent says.
British Foreign Secretary William Hague said there would "undoubtedly" be British nationals caught up in Saturday's events, while the US State Department said it had reports that American citizens were injured in what it called "a senseless act of violence".
Two French citizens and two Canadians, including a diplomat, are also among the dead.
Nairobi's mortuary superintendent, Sammy Nyongesa Jacob, told Reuters that Africans, Asians and Caucasians were among the bodies brought to the mortuary.
This is one of the worst incidents in Kenya since the attack on the US embassy in August 1998.
At night descended outside the shopping complex, the siege continued
Many of those who were inside the Westgate centre when the gun battle began managed to flee, but some were trapped.
Armed police combed the corridors as terrified shoppers fled.
This woman who had been held by the gunmen was carried out of the building in a state of shock by the emergency services.
Some went to extraordinary lengths to escape.
This pregnant woman was separated from her husband and two-year-old daughter during the attack. She hid with about 20 others on the roof of the building and was eventually rescued by police and reunited.
Security forces went from shop to shop to secure the building.
Two contingents of army special forces troops are reported to have moved inside the mall as dusk fell.