Al-Qaeda-linked Islamist militants said Tuesday they were still holding hostages as Kenyan troops battled for a fourth day to end the bloody siege at a Nairobi shopping centre.

Sporadic gunfire and a series of explosions at the upmarket Westgate mall broke out again at dawn, hours after officials claimed Kenyan troops had wrested back "control" of the sprawling complex from Somalia's Shebab insurgents, who are said to include Americans and a British woman.

At least 65 shoppers, staff and soldiers have been killed and close to 200 wounded in the siege, but concerns are high that the toll may rise, with the Shebab boasting about "countless number of dead bodies still scattered inside the mall".

The fate of 63 people listed as missing remains unclear.

"The hostages who were being held by the mujahedeen inside Westgate are still alive, looking quite disconcerted but, nevertheless, alive," the Shebab said in their latest Twitter message.

However, Kenyan officials have said all the hostages are believed to have been freed, with the interior ministry saying Tuesday the assault was "very near the end".

Security sources said "one or two" militants were barricaded in or around a casino on one of the upper floors of the complex.

Meanwhile, explosive experts were defusing devices set up by the militants, police said, adding another dangerous element to the siege, which has now dragged on for over 72-hours.

Part of the mall's rooftop parking also collapsed on Tuesday, security sources said, following a fierce fire the day before.

Shebab fighters stormed the crowded mall midday on Saturday, tossing grenades, firing automatic weapons and sending panicked shoppers fleeing.

Kenyan Foreign Minister Amina Mohamed said among the fighters were several American nationals and a British woman, which media reports have speculated could be a Muslim convert known as the "White Widow".

Government spokesman Manoah Esipisu told AFP that special forces were now "sanitising" the complex in case "there are a couple of them hiding in a remote room or corner".

"We think that everyone, the hostages, have been evacuated," Esipisu said.

Special forces on Monday killed at least three gunmen and wounded several in bitter fighting in the part Israeli-owned complex, popular with wealthy Kenyans and expatriates.

Three Kenyan soldiers on Tuesday died from injuries sustained in those gun battles, the army said. Eight others remain in hospital.

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

'White Widow' in spotlight

In an interview with US public broadcaster PBS, Kenya's foreign minister said Americans and a British woman were among the attackers.

"The Americans, from the information we have, are young men, about between maybe 18 and 19," Mohamed said.

Asked if the Briton was a woman, she replied: "Woman. And she has, I think, done this many times before."

Interior Minister Joseph Ole Lenku had said earlier that all the attackers were men but "some of them had dressed like women."

Britain's Home Secretary Theresa May said she was aware of the reports, adding: "But until we can see the investigation is completed it is not possible to give further details or to confirm or deny that issue."

There is growing media speculation at the role of wanted British extremist Samantha Lewthwaite, daughter of a British soldier and widow of suicide bomber Germaine Lindsay, who blew himself up on a London Underground train on July 7, 2005, killing 26 people.

Lewthwaite is wanted in Kenya, and is accused of links to the Shebab.

A Kenyan security source and a Western intelligence official said Israeli forces were involved in operations to end the mall siege, along with British and US agents.

Police also said they hadarrested more than 10 people for questioning.

Kenyan President Uhuru Kenyatta has called the attack "despicable and beastly".

Shebab spokesman Ali Mohamud Rage has said the carnage was in retaliation for Nairobi's two-year battle against the extremists bases in southern Somalia, warning that Kenya will not be at peace "as long as your boys are in our lands."

Non-Muslims selected for execution

Shocked witnesses said the attackers tried to weed out non-Muslims for execution by demanding they recite the Shahada, the Muslim profession of faith. Children were also executed.

As well as scores of Kenyans -- from ordinary workers to the president's nephew -- the dead include six Britons including a British-Australian, two Canadians including a diplomat, a Chinese woman, a Dutch woman, two French women, two Indians, a South African and a South Korean.

Also killed was Ghanaian poet and former UN envoy Kofi Awoonor.

"The people who did this, they are vigilantes, they are animals," British businessman Louis Bawa, whose eight-year-old daughter and wife were killed, told the Daily Telegraph.

Security camera footage seen by Kenyan media showed gunmen firing a barrage of bullets as they moved through the mall.

Away from Westgate, Nairobi on Tuesday appeared to have returned to largely business as usual, but the attacks have shocked Kenyans deeply.

Blood donor appeals ended after banks filled with donations from hundreds, while over $650,000 (490,000 euros) has been raised to support the families affected.

In Kenya's port city Mombasa, security was tight for the latest hearing in the long-running trial of suspected British Islamist militant Jermaine Grant on explosives charges.

Israeli interests in Kenya have come under attack before, and the Westgate mall -- frequented by well-to-do Kenyans, diplomats, UN workers and other expatriates -- has long been seen as a potential target.

The siege, which has revived memories of the 2008 Mumbai attacks, is the worst attack in Nairobi since an Al-Qaeda bombing at the US embassy killed more than 200 people in 1998.

US President Barack Obama, whose father was Kenyan, has called Kenyatta offering "whatever law enforcement support that is necessary".