Sporadic gunfire and explosions have been heard from the Westgate shopping centre in Nairobi, four days after Islamist militants began an assault in which more than 60 people were killed.
A military commander at the scene has told the BBC he believes there could still be two or three gunmen inside. Police say six attackers have been killed.
At least 62 shoppers and staff have been killed, with more than 170 in hospital, and there are fears the death toll will rise.
Kenyan Foreign Minister Amina Mohamed says the militants include at least two Americans and a British woman.
Earlier, Interior Minister Joseph Ole Lenku said the operation would come to an end soon.
"We are in control of all the floors, the terrorists are running and hiding in some stores ... there is no room for escape," he said, adding that some hostages had been freed, but without giving specific numbers.
Kenyan troops stormed the building early on Monday. Israeli forces are also reported to have been involved in the operation, along with British and US agents.
The Somali Islamist al-Shabaab movement has said it carried out the attack in retaliation for Kenyan military operations in Somalia. About 4000 Kenyan troops are in the south of Somalia, where they have been fighting al-Shabaab since 2011.