The Al-Qaeda-linked fighters, in a message posted on Twitter, said "137 hostages who were being held by the mujahedeen" had died.

They also accused Kenyan troops of using "chemical agents" to end the four-day stand-off.

"In an act of sheer cowardice, beleaguered Kenyan forces deliberately fired projectiles containing chemical agents," one tweet read.

"To cover their crime, the Kenyan government carried out a demolition to the building, burying evidence and all hostages under the rubble."

President Uhuru Kenyatta announced an end to the 80-hour bloodbath late Tuesday, with the "immense" loss of 61 civilians and six members of the security forces.

Police said the death toll was provisional, with the Kenyan Red Cross listing 63 people as still missing.

There was no immediate response from Kenya's government, but the Shebab have in past made repeated outlandish claims, especially on their Twitter site.

The Shebab said they carried out the attack in retaliation for Kenya's two-year battle against the extremists' bases in the country.

In one of the worst attacks in Kenya's history, the militants marched into the four-storey, part Israeli-owned mall at midday Saturday, spraying shoppers with automatic weapons fire and tossing grenades.

Kenya on Wednesday began three days of official mourning, with flags flying at half mast, while rescue workers scoured the wreckage of the mall for bodies.

Close to 200 were wounded in the four-day siege, which saw running battles between militants and security forces in the complex, Nairobi's largest shopping centre and popular with wealthy Kenyans, diplomats, UN workers and other expatriates.