Kenyan troops battled into the early hours of Monday as they tried to end a bloody stand-off with Somali Islamist militants holding hostages inside a shopping mall, with police warning the death toll of 68 could rise sharply.

The army said it had secured most of the upmarket, part Israeli-owned Westgate complex, and that most the hostages had been rescued. It said it was trying to bring a "speedy conclusion" to the drama, now into its third day.

Security and intelligence sources told AFP that Israeli agents were also assisting in the operation. Kenya's National Disaster Operation Centre said a "major engagement" with the Al Qaeda-linked Shebab fighters was in process.

"Our concern is to rescue all hostages alive and that is why the operation is delicate," the Kenya Defence Forces said in its latest update. It did not say how many people were being held by the dozen-or-so attackers.

"All efforts are underway to bring this matter to a speedy conclusion," it said, adding four of its soldiers were wounded in what appeared to be the final efforts to secure the mall, which is popular with wealthy Kenyans and expatriates.

An AFP correspondent close to the mall said the area was eerily quiet, with no sounds of gunshots heard -- possibly indicating the attackers were holed up deep inside the sprawling four-storey complex, one of Nairobi's largest buildings.

"The criminals are now all located in one place within the building," Kenyan President Uhuru Kenyatta said in a speech to the nation.

"They shall not get away with their despicable and beastly acts," Kenyatta said in an emotional speech, in which he announced he had lost a nephew and his fiancée in the attack. "We will punish the masterminds swiftly, and indeed very painfully."

Kenyatta said more than 1,000 people were rescued, and that he had also received "numerous offers of assistance from friendly countries."

A Kenyan security source said Israelis "are rescuing the hostages and the injured". The Israeli foreign ministry refused to confirm or deny its agents were involved, although a Western intelligence official confirmed the Israelis were playing a frontline role.

British and US agents were also at the scene, the source said.

BODIES STILL INSIDE

Terrified witnesses told of scenes of horror and panic as the masked gunmen tossed grenades and sprayed automatic gunfire in the packed centre around midday on Saturday, sending panicked shoppers and staff fleeing or diving for cover.

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," Shebab spokesman Sheik Ali Mohamud Rage said in a statement.

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".

Witnesses have confirmed that the gunmen were trying to weed out non-Muslims for execution by interrogating people on their faith.

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.

'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. "I have never witnessed this in my life."

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.

One teenage survivor told how he played dead to avoid being killed.

"I heard screams and gunshots all over the place. I got scared... (and) hid behind one of the cars," 18-year-old Umar Ahmed told AFP.

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.

The attack is the worst in Nairobi since an Al-Qaeda bombing at the US embassy killed more than 200 people in 1998.

It was condemned by world powers.

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, his lawyer said.