Troops and armed police have completely surrounded the Westgate centre
Kenyan security forces say they have taken control of all floors of the Nairobi shopping centre attacked by suspected al-Shabab militants.
An explosion and bursts of gunfire were heard coming from the complex on Tuesday morning as speculation grew that the operation was nearing its end.
At least 62 people have been killed with more than 170 injured.
Meanwhile, Kenya's foreign minister said "two or three" Americans and a British woman 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."
He said it was "unlikely" that any hostages were still in the building.
Fresh gunfire As night fell on Monday, flames and thick smoke continued to rise from the building an hour after four large explosions shook the neighbourhood.
At about 06:30 (03:30 GMT) on Tuesday a reporter with the Associated Press said another explosion and more gunfire could be heard.
Security forces removed another body from the mall, which remained on fire, AP reported.
Kenyan special forces were still battling "one or two" militants holed up on one of the upper floors, security sources told an AFP correspondent at the scene.
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 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.