Thick black smoke billowed from the Westgate mall as Kenyan officials said the more than two-day-long siege -- in which the gunmen have massacred at least 62 people and taken dozens more hostages -- was close to being resolved.

"We think the operation will come to an end soon," Interior Minister Joseph Ole Lenku told reporters camped outside the vast complex, which was popular with wealthy Kenyans and expatriates.

"We are in control of all the floors," he said. "The terrorists are running and hiding in some stores... There is no room for escape."

Lenku said most hostages had been freed, without giving specific numbers.

At least 11 Kenyan troops were wounded in Monday's gun battles, the army said.

Plumes of smoke continued to dominate Nairobi's skyline as night fell on the third day, although the interior ministry said the fire was under control.

The Kenyan Red Cross said at least 63 people were recorded missing, thought to include hostages as well as those possibly killed or still hiding. Around 200 people were wounded, officials said.

Three gunmen were also killed in the fighting and several wounded, while police said they had arrested more than 10 people for questioning.

Somalia's Al Qaeda-linked Shebab insurgents have claimed the attack, which began midday on Saturday, when the gunmen marched into the complex, firing grenades and automatic weapons and sending panicked shoppers fleeing.

Kenyan army chief Julius Karangi said the gunmen were of different nationalities. Many foreign fighters, including Somalis with dual nationalities, are members of the Shebab force.

Kenyan President Uhuru Kenyatta, whose nephew was killed along with his fiancée, has vowed that the attackers will "not get away with their despicable and beastly acts."

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