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Troops could be seen on the move in the area surrounding the mall before dawn on Monday morning
Heavy gunfire and explosions have been heard at the shopping centre in Nairobi where militants are believed to be holding a number of hostages.
Sixty-eight people have been killed and more than 170 injured since the attack began on Saturday.
Between 10 and 15 attackers - thought to be militants from the Somali al-Shabab movement - are still inside the Westgate shopping centre.
Reporters at the scene said there had been heavy and rapid bursts of fire.
The BBC's Mike Wooldridge in Nairobi says that the battle to end the long stand-off is continuing in earnest as conditions for those trapped inside the complex deteriorate.
An unnamed Kenyan security source told the AFP news agency that an army assault was underway.
An AFP correspondent at the scene said he heard about 15 minutes of fierce gunfire which then subsided.
A photographer accompanying the correspondent said troops deployed around the mall were forced to duck for cover.
The photographer said it "sounded as if the shots were coming from somewhere around the mall, or were being fired from a vantage point in the mall".
The defence forces said on Twitter several hours ago: "All efforts are under way to bring this matter to a speedy conclusion."
Authorities have emphasised that it is a delicate operation as the safe rescue of the hostages is their top priority, says our correspondent.
'More bodies'
Overnight reports said that the gunmen were holed up in a supermarket.
Earlier defence spokesman Col Cyrus Oguna said only a small number of hostages were still being held and most had been rescued.
Those trapped are either as hostages or in hiding.
As troops continue to clear the building it was possible they would come across more bodies, Col Oguna warned on Sunday.
In a news conference on Sunday, Kenyan President Uhuru Kenyatta said the country was united and strong in adversity.
"The criminals are now located in one place within the building," he said.
"With the professionals on site, we have as good a chance to neutralise the terrorists as we could hope for," he said.
Mr Kenyatta said his nephew and the man's fiancee were among the dead.
The UK Foreign Office has confirmed that three Britons have been killed, and says the number is likely to rise.
British Prime Minister David Cameron called it "an absolutely sickening and despicable attack of appalling brutality".
US President Barack Obama called President Kenyatta on Sunday to express condolences and reiterate "US support for Kenya's efforts to bring the perpetrators of the attack to justice".
The wife of an American working for the US Agency for International Development was killed, US officials said.
Prominent Ghanaian poet Kofi Awoonor - who was attending a literary festival in Nairobi - also died, as did a Chinese woman.
French, Dutch, South African, Indian and Canadian nationals are also among the foreigners confirmed killed, along with a dual Australian-British national.
Thousands of Kenyans responded on Sunday to appeals for blood donations.
Al-Shabab says it carried out the attack in response to Kenyan military operations in Somalia.
The group, 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.
There are about 4,000 Kenyan troops in the south of Somalia, where they have been fighting the militants since 2011.