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 troops were combing the Westgate complex and it is "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.
The Kenyan Red Cross has told the BBC that 63 people remain unaccounted for.
It is unclear how many militants are in the 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."
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.
