23/09/2013 68 people have been reported dead 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.
News from Nairobi says that the battle to end the long stand-off is continuing in earnest as conditions for those trapped inside the complex deteriorate.
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With the professionals on site, we have as good a chance to neutralise the terrorists as we could hope for”
Uhuru Kenyatta Kenyan president
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.
[Adapted from BBC]