Kenya Mall Shooting: At Least 59 Killed, 175 Injured in 'Senseless Act of Violence'
Joe Lenku said 1,000 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.
It is not known how many civilians remain trapped there - either as hostages or hiding from the militants.
There are reports that the gunmen are currently holed up in a supermarket.
The Somali militant group al-Shabab says it carried out the attack on the upmarket shopping centre in response to Kenyan military operations in Somalia.
There are about 4,000 Kenyan troops in the south of Somalia, where they have been fighting the militants since 2011.
'Watching and monitoring'
Kenyan officials said "major operations" were under way with police and soldiers preparing an apparent bid to bring an end to the stand-off.
But Joe Lenku, Kenya's interior minister, stressed that the operation was "very, very delicate".
"The priority is to save as many lives as possible,'' he said.
The BBC's Will Ross at the scene said it would be extremely difficult for the military do a quick raid on the building because of all the people inside.
Al-Shabab has claimed there are at least 36 hostages, but this cannot be independently confirmed. There are also likely to be people hiding away from the attackers.
Our correspondent says the full extent of the attack will not be known until the military is back in control.
Meanwhile, people are still escaping from the building.
Cecile Ndwiga got out on Sunday morning, saying she had been hiding under a vehicle in the basement car park but could not leave earlier because "the shootout was all over - left, right".
The authorities have asked journalists to exercise caution when reporting military developments because the gunmen might be monitoring the media.
"Hostiles suspected to have access to the internet," the Disaster Operation Centre in Nairobi posted on Twitter.
"Reports on personnel movement and progress will not be posted for fear of compromising strategy."
The authorities are also appealing for Kenyans to donate blood. Big queues have formed at a Nairobi donation centre.
The attack began at about 12:00 local time (09:00 GMT) on Saturday, when the militants entered the Westgate centre, throwing grenades and firing automatic weapons. A children's day was being held at the time - children are among those reported killed.
Witnesses report seeing many bodies strewn round tables of unfinished fast food - with pop music left playing in the background.
Some witnesses said the militants told Muslims to leave and said non-Muslims would be targeted.
"They came and said: 'If you are Muslim, stand up. We've come to rescue you'," said Elijah Lamau.
He said the Muslims left with their hands up, and then the gunmen shot two people.
BBC security correspondent Frank Gardner says a security source told him that at least one of the attackers was a woman who appeared to have a leadership role.
Foreigners among dead
In a televised address on Saturday evening, Mr Kenyatta said: "We shall hunt down the perpetrators. We shall get to them and we shall punish them for this heinous crime."
He said he had "personally lost family members in the Westgate attack".
British Foreign Secretary William Hague said there would "undoubtedly" be British nationals caught up in Saturday's events, while the US State Department said it had reports that American citizens were injured in what it called "a senseless act of violence".
Two French citizens and two Canadians, including a diplomat, are also among the dead.
Prominent Ghanian poet Kofi Awoonor - who was was attending a literary festival in Nairobi - also died, as has a Chinese woman.
Security experts are reported to have warned that the Israeli-owned complex was in danger of being subjected to a terror attack.
Al-Shabab, which is part of the al-Qaeda network, has repeatedly threatened attacks on Kenyan soil if Nairobi did not pull its troops out of Somalia.
The BBC's Mark Doyle, who is embedded with the African Union (AU) mission in Somalia, says AU troops attack al-Shabab where they can.
Al-Shabab believes the AU forces are invaders stopping their legitimate vision of creating an Islamic state - and the group responds by mounting hit-and-run attacks, our correspondent says.
This is one of the worst incidents in Kenya since the attack on the US embassy in August 1998.