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".
Ms Mohamed appeared to contradict earlier comments from Kenya's interior minister, who suggested that all the attackers were men - though some may have been dressed as women.
The BBC's Mike Wooldridge in Nairobi says Ms Mohamed's remarks have fuelled media speculation about the possible involvement of Samantha Lewthwaite, the widow of one of the men who carried out attacks on London's transport system on 7 July 2005.
British officials said they would not be drawn on the identity of the attackers while investigations continue.
The Kenyan Red Cross has told the BBC that 63 people remain unaccounted for.
Early on Tuesday a Kenyan officer at the scene said he believed there could be two or three attackers left inside the building.
Kenyan officials said earlier that three "terrorists" had been killed, and that 10 people had been arrested.
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.
As night fell on Monday, flames and thick smoke continued to rise from the building an hour after four large explosions shook the neighbourhood.
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.