Kenyan police and army units moving through the shattered Westgate Mall in Nairobi continue to find dead and wounded shoppers. The death toll now stands at 59 with 175 wounded.
Police are saying that there may be as many as 15 attackers still in the building, armed with automatic rifles and grenades. It is also thought that there are about 30 shoppers still in the mall, trapped and unable to flee. Authorities are saying they don't know if there are any living hostages.
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.
The UK Foreign Office has confirmed that three Britons are among the dead, and says the number is likely to rise.
French, Chinese, Ghanaian and Canadian citizens are also among the foreigners confirmed killed.
British Prime Minister David Cameron called it "an absolutely sickening and despicable attack of appalling brutality".
There is a heavy military presence both in and around the shopping centre. Sporadic gunfire can be heard from inside.
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.
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 Mr Lenku 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.
Perhaps the most interesting development is the acknowledgment that Israeli advisors are on site working with Kenyan authorities to bring the tragedy to a successful conclusion:
Israeli advisers are helping Kenya formulate a strategy to end a siege at a Nairobi shopping mall where Islamist militants have killed at least 59 people and are holding hostages, an Israeli security source said on Sunday.
"There are Israeli advisers helping with the negotiating strategy, but no Israelis involved in any imminent storming operation," said the source, who declined to be identified.
The source said only a "handful" of Israelis, "purely in an advisory role," were on scene at the upscale Westgate shopping center, which has several Israeli-owned outlets and is frequented by expatriates and Kenyans.
An Israeli source in Nairobi said all Israelis who were in the mall at the time of the attack had made it out safely, with the last three rescued overnight.
There were conflicting reports from other security sources in Nairobi about the part Israel was playing.
One Kenyan security source, who asked not to be identified, told Reuters that the Israeli military was involved in the operation, while a private security official also said they were helping comb the mall.
But the Kenyan Interior Minister insisted it was a national operation, despite offers of foreign support.
Al-Shabab is turning out to be one of the deadliest terror groups around. They appear to be getting at least some of their arms from Iran, which would explain Israel's interest in combatting them. They also seem willing to carry out attacks in other countries, which sets them apart from other terrorist groups.
The US has been carrying out a low intensity drone war in Somalia, mostly targeting al-Shabab. It would seem urgent to pick up the pace of our attacks given the lethality of this terrorist act.