Agents from US, Britain and other countries assist local teams as Kenyan government puts death toll at 72

US, British and Israeli agencies are helping Kenya investigate an attack by Islamist militants on a Nairobi shopping mall that killed at least 72 people and destroyed part of the complex.

After a four-day siege, President Uhuru Kenyatta said on Tuesday troops had defeated the al Qaeda-linked al Shabaab group that targeted the shopping centre popular with prosperous Kenyans and foreigners. He declared three days of mourning.

The attack has highlighted the reach of the Somali al-Shabaab and the capabilities of its crack unit believed to be behind the bloodshed in Westgate mall, confirming international fears that as long as Somalia remains in turmoil it will be a recruiting and training ground for militant Islam.

The militants stormed the mall, known for its Western shops selling iPads and Nike shoes, in a hail of gunfire and grenades at lunchtime Saturday. The attack ended on Tuesday when Kenyan troops detonated explosives to get through locked doors inside the mall as they searched for militants or booby traps.

"We have moved to the next phase," interior minister Joseph ole Lenku told a news conference.

He said that alongside US, British and Israeli agencies, Kenya was also receiving help from Germany, Canada and the police agency Interpol in the investigation.

He said he did not expect the death toll of 61 civilians, six members of the security forces and five attackers to rise significantly, and that the only bodies still likely to be found were those of slain assailants.

Three floors collapsed after the blasts and a separate fire weakened the structure of the vaulted, marble-tiled building. Officials said the blaze arose from militants lighting mattresses as a decoy.

Kenya has said 10 to 15 attackers launched the raid. Ole Lenku said the investigation would seek to ascertain if there were any females among the assailants, as some witness accounts suggest, and would also see if the groups had rented a store in the mall prior the attack as part of their preparation.

Al-Shabaab said it launched the assault to demand Kenya withdraw its troops fighting with African peacekeepers in Somalia. It said hostages were killed when Kenyan troops used gas to clear the mall. Officials dismissed this as "propaganda".

Kenyatta has said Kenyan forces would not leave Somalia. "We have ashamed and defeated our attackers," he said in his televised address on Tuesday.

US president Barack Obama, whose father was Kenyan, said he believed the country – scene of one of al Qaeda's first big attacks, in 1998, when a bomb devastated the US embassy in Nairobi – would continue to be a regional pillar of stability.

"The investigators will be looking to see what information they can extract to identify the terrorists and their nationalities, including DNA tests," a senior official from the National Disaster Operation Centre told Reuters, after officials described the attack as a "multinational" operation.

Eleven people suspected of involvement with the well-planned assault are in custody, but Kenyan officials have not said how many, if any, were gunmen taken alive and how many may have been people arrested elsewhere.

It was unclear whether intelligence reports of American or British gunmen would be confirmed. Al-Shabaab denied that any women took part, after British sources said the fugitive widow of one of the 2005 London suicide bombers might have some role.

In Washington, US attorney general Eric Holder said on Wednesday there had been no verification that Americans were involved in the mall attack.

A thin trail of smoke still drifted up on Wednesday above the Israeli-built shopping complex, a symbol of Africa's economic rise that has drawn in foreign investors.

Faster growth has also created wider wealth gaps, adding to grievances tapped by several violent Islamist groups from Mali to Algeria and Nigeria to Kenya. All have espoused an anti-Western, anti-Christian creed.

"If Westgate was Kenya's symbol of prosperity, it is now a symbol of their vulnerability, a symbol of defeat and overall Kenyan impotence," al-Shabaab said on its Twitter account, one of several taunts it sent after the attack.

Al-Shabaab, which derided Kenya as it was battling militants inside the mall, said action by Kenyan troops using gas were responsible for the "lives of the 137 hostages who were being held by the mujahideen [fighters]." The Kenyan government puts the casualty toll at 72, although this is likely to rise.

Ole Lenku said he could not confirm intelligence reports of British and American militants. One cabinet minister had earlier denied speculation that women were among the guerrillas, but said some had been dressed as women, a possible ploy to get weapons past the mall's unarmed private security guards.

A British security source said it was possible Samantha Lewthwaite, widow of one of the London suicide bombers of 7 July 2005, was involved in the Nairobi siege. "It is a possibility. But nothing definitive or conclusive yet," the source said.

Lewthwaite is wanted in connection with an alleged plot to attack expensive hotels and restaurants in Kenya.

Kenyatta thanked other leaders, including Obama, for their support and used his address to praise the response of the Kenyan people and call for national unity, six months after his election was marked by ethnic tensions.

• An earlier version of this article, by the Associated Press, gave more weight to claims by al-Shabab of the responsibility of the Kenyan government for a high death toll. The article was updated to give greater context.