Kenyan security forces say they are attempting to clear the Westgate shopping complex in Nairobi in order to bring to an end the three-day siege.
Explosions and heavy gunfire were reported earlier as soldiers stormed the mall, where suspected al-Shabab militants are thought to be holed up.
The Kenya Defence Forces (KDF) said three “terrorists” had been killed and all escape routes sealed off.
Flames and thick smoke are continuing to rise from the building.
The KDF said the fire had been started by “terrorists to distract the ongoing operation”, and that the blaze was being managed by firefighters.
A number of countries are believed to have offered assistance to the Kenyan authorities currently dealing with the siege at the Westgate Mall.
Kenya is seen as a largely pro-Western country in a strategically important continent that is facing growing instability from the threat of Islamic extremism.
Western interests in Kenya have also been targets in the past – most notably the 1998 attack on the US embassy in Nairobi carried out by al-Qaeda.
However, at present, Kenya’s forces are taking the lead in the hostage crisis. If there is any involvement by foreign nations, it’s likely to be in a purely advisory role. It has already been reported that Israeli “security specialists” are on the ground in Nairobi giving advice, although this has not officially been confirmed.
Even if foreign forces are giving advice or even more, the Kenyan authorities are unlikely to want to give the impression that they cannot deal with this crisis themselves.
The official death toll stands at 62 and more than 170 have been injured.
The Somali Islamist al-Shabab movement has said it carried out the attack in retaliation for Kenyan military operations in Somalia.
The BBC’s Mike Wooldridge in Nairobi says the number of militants involved in the attack was put at between 10 and 15, and officials say some of them are still on the run, hiding in shops.
The Kenyan government says almost all the hostages have been evacuated from the Westgate shopping centre – but it is not clear whether any are still in the hands of the militants.
And that may be one of the reasons the authorities say they are still moving cautiously, trying to ensure that there is no further loss of life, our correspondent says.
The KDF said 10 bodies had been retrieved from the building in the last 24 hours. More than 200 civilians have been rescued, 65 of whom remain in hospital.
Eleven KDF soldiers were injured during the operation, it said.
Earlier, police used tear gas to disperse crowds of onlookers gathered close to the Westgate Centre.
The Interior Ministry is issuing regular warnings for people to stay away for their own safety.
Security has also been stepped up at entrance and exit points across the country, with “more than 10 individuals” arrested in relation to the attack, the ministry said.
However, it did not specify when or where the arrests were made.
Thick black smoke started billowing from the building shortly after blasts were heard
The Kenyan interior minister said security forces were gaining an advantage over the militants
Kenyan police officers took position around the Westgate Shopping Centre
Police fired tear gas to try to disperse crowds of onlookers near the centre.
More than 1,000 people were inside the mall complex when the attack began on Saturday.
Dr Sunil Sachdeva, a dentist who runs a clinic inside the mall, described the scene as the attack unfolded.
“There was a tent where a cookery competition for children was carrying on and there were bodies lying under there,” he told the BBC