DHAKA: Kenyan security forces say they have taken control of all floors of the Nairobi shopping centre attacked by suspected al-Shabab militants.
The interior ministry said it was "unlikely" any hostages were left in the building.
At least 62 people have been killed with more than 170 injured and there are fears the death toll will rise.
Meanwhile, Kenya`s foreign minister said "two or three" Americans and one Briton were among the attackers.
In an interview with the US TV programme PBS Newshour, Amina Mohamed said the Americans were 18 or 19 years old of Somali or Arab origin and lived "in Minnesota and one other place". She said the Briton was a woman who has "done this many times before".
The Kenyan Red Cross has told the BBC that 63 people remain unaccounted for.
It is unclear how many militants are in the Westgate building but Kenyan officials said three "terrorists" had been killed.
The Somali Islamist al-Shabab movement has said it carried out the attack in retaliation for Kenyan military operations in Somalia.
Kenyan Interior Minister Joseph Ole Lenku told the BBC late on Monday that the operation would continue overnight, but stressed it was in its final stages.
"The terrorists could be running and hiding in some stores, but all floors now are under our control," he said.
"There is no room for escape."
Smoke rises from Westgate centre. 23 Sept 2013 A fire was raging somewhere inside the Westgate on Monday
As night fell on Monday, flames and thick smoke continued to rise from the building an hour after four large explosions shook the neighbourhood.
A witness said the smoke was pouring through a skylight inside the main department and grocery store where mattresses and other goods appeared to have been set on fire.
The Kenya Defence Forces said the fire had been started by "terrorists to distract the ongoing operation".
Between 12 and 15 militants stormed the Westgate centre on Saturday, throwing grenades and firing on shoppers and staff.
At least 18 foreigners are among the dead, including six Britons, as well as citizens from France, Canada, the Netherlands, Australia, Peru, India, Ghana, South Africa and China.
Nearly 200 people were wounded, including five Americans.
President Obama says the US stands with Kenya
President Barack Obama called the attack a "terrible outrage" and said the US was providing all the co-operation it could to Kenya.
Thousands of Kenyans have been responding to appeals for blood donations.
Al-Shabab, which is linked to al-Qaeda, has repeatedly threatened attacks on Kenyan soil if Nairobi did not pull its troops out of Somalia.
There are about 4,000 Kenyan troops in the south of Somalia as part of an African Union force supporting Somali government forces.
Al-Shabab is fighting to create an Islamic state in Somalia.
Despite being pushed out of key cities in the past two years, it remains in control of smaller towns and large swathes of the countryside.
Source: BBC
BDST: 1001 HRS, SEP 22, 2013
RS/BSK