Kenyan security forces said last evening they were attempting to clear the Westgate shopping complex in Nairobi in order to bring to an end to the three-day siege.
Explosions and heavy gunfire were reported earlier as soldiers stormed the mall, where suspected al-Shabaab militants were thought to be holed up.
The Kenya Defence Forces (KDF) said three “terrorists” had been killed and all escape routes sealed off.
Flames and plumes of smoke continued to billow 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.
The official death toll stands at 62 with more than 170 people injured.
The Somali Islamist al-Shabaab has said it carried out the attack in retaliation for Kenyan military operations in Somalia.
The Kenyan interior ministry put the number of militants involved in the attack at between 10 and 15, and officials say some of them are still at large.
The Kenyan government says almost all the hostages had been evacuated from the Westgate shopping centre, but it was not clear whether any were 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, the BBC said.
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.
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. 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. “There’s a famous radio presenter in Kenya, she was shot. The scene was carnage and there was a guy lying right in the corner. He was cut to shreds.”
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 have been responding to appeals for blood donations.
Al-Shabaab, 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 southern Somalia, where they have been fighting the militants since 2011.
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