Heavy gunfire and loud explosions erupted at Nairobi's Westgate shopping mall today as Kenyan troops fought Al Qaeda-linked gunmen who were holding hostages after massacring at least 69 people.

The Red Cross said at least 63 people were recorded missing, thought to include hostages as well as those possibly killed or still hiding in the 48-hour-long siege.

As the stand-off entered its third day, sustained bursts of rapid gunfire broke out at dawn, and soldiers posted around the complex ducked for cover. This was followed by explosions and more sporadic weapons fire, AFP correspondents at the scene said.

The Kenyan army said it had secured most of the upmarket, part Israeli-owned complex, while a security official said a final assault was underway against the Somali Shebab rebels, believed to be pinned down in a part of the mall but using hostages as human shields.

"We have managed to rescue more hostages overnight and very few are remaining," Kenyan police chief David Kimaiyo said today, in the latest of a string of upbeat statements. "We are also closing in on the attackers."

Officials have not said how many people were being held by the dozen-or-so attackers, who marched into the sprawling four-storey complex at midday Saturday, spraying shoppers with machine gun fire and tossing grenades.

Shebab spokesman Ali Mohamud Rage warned the hostages would "bear the brunt of any force directed against the mujahedeen".

However, Kenyan President Uhuru Kenyatta has vowed the attackers will "not get away with their despicable and beastly acts."

"We will punish the masterminds swiftly, and indeed very painfully," he vowed in a speech Sunday, revealing that a family member -- a nephew and his fiancee -- were among the dead.

A Kenyan security source and a Western intelligence official said Israeli forces were involved in the operation, along with British and US agents.