At least 59 people were killed and 175 injured in Saturday's attack on a Nairobi shopping centre, a Kenyan government minister has said.
Joe Lenku said 1000 people had managed to escape from the Westgate centre after the assault by suspected al-Shabab militants.
He added that between 10 to 15 attackers were still in the building.
An unknown number of hostages are still inside the mall - either as hostages or hiding from the militants.
There are reports that the gunmen are currently holed up in a supermarket.
Kenyan President Uhuru Kenyatta earlier vowed to "hunt down the perpetrators wherever they run to".
The BBC reports the al-Shabab group says the attack is revenge for Kenya's role in fighting the group in Somalia.
The Westgate centre came under attack by al-Shabab fighters at about midday on Saturday when grenades were thrown inside.
News agencies report that gunmen ordered Muslims to leave and that non-Muslims would be targeted.
Kenyan officials said "major operations" were under way with police and soldiers preparing an apparent bid to bring an end to the stand-off.
They said the security forces had finally "pinned down" the surviving gunmen.
Al-Shabab has claimed there are at least 36 hostages, but this cannot be independently confirmed and there are also likely to be people hiding away from the attackers.
Army marksmen are all around the mall. Troops are also in place.
Police earlier urged residents to stay away from the area and told media outlets to stop live transmissions from the scene.
Six hours after the attack began, Secretary for the Interior Joseph ole Lenku said the security situation was "under control".
He urged the public "not to speculate" about the nature of the attack and said most people had been evacuated.
In a television address to the nation, President Uhuru Kenyatta said: "We have overcome terrorist attacks before. We will defeat them again."
Mr Kenyatta said some of his relatives were among those killed and those responsible will be brought to justice.
The al-Shabab group, which is linked to al Qaeda, says its fighters carried out the attack.
"There will be no negotiations whatsoever at #Westgate," said Al-Shabab on Twitter.
Kenya has about 4000 troops in the south of Somalia, where they have been fighting al-Shabab since 2011.
Casualties
Some of the wounded were wheeled out on stretchers and shopping trolleys. Many had multiple light wounds. Dozens were ferried away by ambulance.
"I have counted 25 dead, and that is just from the mall alone," said Red Cross secretary general Abbas Guled earlier.
