Heavy gunfire and loud explosions erupted at Nairobi's Westgate shopping mall Monday as Kenyan troops fought Islamist militants who were holding hostages after massacring at least 68 people.

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 three big 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 source said a final assault was underway against the Al-Qaeda-linked Somali Shebab rebels, believed to be pinned down in a part of the mall but using hostages as human shields.

"Our concern is to rescue all hostages alive and that is why the operation is delicate," the Kenya Defence Forces said in a statement overnight, adding that it was trying to bring a "speedy conclusion" to the drama.

It did not say 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".

In an address to the nation on Sunday, Kenyan President Uhuru Kenyatta 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, 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.

Bodies still inside

Terrified witnesses told of scenes of horror and panic as the masked gunmen stormed in. Officials estimated some 200 people have been wounded, and the Red Cross made a nationwide appeal for blood donors.

Police sources who had entered the building on Sunday evening said they feared that death toll, now confirmed at 68, "could be much, much higher...

judging from the bodies sighted inside."

Somalia's Shebab rebels said the carnage was in retaliation for Kenya's military intervention in Somalia, where African Union troops are battling the Islamists.

"If you want Kenya in peace, it will not happen as long as your boys are in our lands," Rage said.

The group also issued a string of statements via Twitter, one of them claiming that Muslims in the centre had been "escorted out by the Mujahideen before beginning the attack".

A number of witnesses have been quoted as saying that the gunmen were trying to weed out non-Muslims for execution by interrogating people on their faith or asking them to say the Shahada, or Islamic creed.

The dead also included three Britons, two French women, two Canadians including a diplomat, a Chinese woman, two Indians, a South Korean, a South African and a Dutch woman, according to their governments. Also killed was Ghanaian poet and former UN envoy Kofi Awoonor, 78, while his son was injured.

Rumours swirled that non-Somalis were among the fighters, but the Shebab said they had released no information about the identies of any of the insurgents.

'People sprayed with bullets'

Mall worker Zipporah Wanjiru, who emerged from the ordeal alive but in a state of shock, said she hid under a table with five other colleagues.

"They were shooting indiscriminately, it was like a movie seeing people sprayed with bullets like that," she said, bursting into tears.

Security camera footage seen by Kenya's The Standard newspaper shows gunmen raking toilet cubicles with a barrage of gunfire, apparently after learning that several people were hidden inside.

Fighters later holed up in a cinema on the top floor and a security room of a supermarket, it added.

Cafe waiter Titus Alede, who risked his life and leapt from the first floor of the mall, said it was a "miracle from God" that he managed to escape the approaching gunmen.

"I remember them saying 'you killed our people in Somalia, it is our time to pay you back'," he said.

Other survivors said they played dead to avoid being killed.

In the hours after the attack began, shocked people of all ages and races could be seen running from the mall, some clutching babies, while others crawled along walls to avoid stray bullets.

Israeli interests in Kenya have come under attack before, and the Westgate mall has long been seen as a potential target.

World powers condemned the attack, which is the worst in Nairobi since an Al-Qaeda bombing at the US embassy killed more than 200 people in 1998.

US President Barack Obama called Kenyatta offering support "to bring the perpetrators of the attack to justice", while UN chief Ban Ki-moon said the violence was "totally reprehensible".

Kenya's Vice President William Ruto has asked the International Criminal Court to delay his trial for crimes against humanity over deadly 2007-08 post-election violence because of the mall standoff, due to resume Monday, his lawyer said. (AFP)