With 62 confirmed dead after al-Shabaab militants stormed the complex, it is unclear whether any hostages are still being held

Kenyan security forces remain locked in a slow and bloody operation to clear Islamist militant hostage-takers from an upmarket shopping mall in Nairobi, as plumes of black smoke pour from the complex and sporadic gunfire and occasional blasts can reportedly be heard.

More than 48 hours after a heavily armed group from the Somalia-based al-Shabaab organisation killed at least 62 people in the Westgate centre, which was packed with shoppers and families, little is known about the situation inside.

The confirmed dead now include four Britons, along with nationals from another dozen countries, as well as Kenya.

Kenya's interior minister, Joseph Ole Lenku, said two of the estimated 10 to 15 militants inside had been killed in an assault by Kenyan commandos, which began on Sunday evening.

The smoke came from mattresses in a supermarket set alight by the militants as a decoy, Lenku said, but declined to give details about the progress of the operation. He told reporters: "We don't want to give you a definitive position on when we think the process will come to an end, but we are doing anything reasonably possible, cautiously though, to bring this process to an end."

All the militants were men, Lenku added, saying some had apparently dressed as women. Some of the initial witness reports from Saturday spoke of seeing female militants.

Kenya's chief of general staff, Julius Karangi, also briefing media, saying the attackers were "clearly a multinational collection from all over the world".

He added: "We have an idea who they are, their nationality and even the number." He did not identify which nations were involved. "We have also have an idea that this is not a local event," he added. "We are fighting global terrorism here and we have sufficient [intelligence] to suggest that."

The fate of any hostages remained unknown, despite briefings that the military operation was nearing an end. While Kenyan officials said on Sunday that "most" of those still in the mall had been rescued, the country's Red Cross said on Monday that 63 people had been reported missing by relatives.

Karangi said Kenyan forces were in charge of all floors in the mall. It remained unclear, however, where the militants were based, and where they might be holding any hostages. Officials initially said the attackers were in a basement supermarket. However, a Kenyan soldier was quoted by Reuters as saying they were dispersed: "They're in the cinema hall, with hostages. There are other terrorists in different parts. They are on the upper floors, the third and fourth floors."

Al-Shabaab, which is demanding Kenya pull its troops out of Somalia, has said it will kill hostages if Kenyan security forces, who are being assisted by Israeli, British and US experts, tried to storm the mall.

"Israelis and Kenyan forces have tried to enter Westgate by force but they could not," said a spokesman, Sheikh Ali Mohamud Rage. "The mujahideen will kill the hostages if the enemies use force."

There were equally chaotic scenes outside the mall complex, where onlookers pushing for a glimpse of the site were showered with teargas by security services attempting to keep them back. Occasional bursts of panic spread through the crowd, sparked by rumours that some attackers might have escaped and were on the loose and by the sporadic volleys of gunfire echoing from inside the shopping centre.

There was more news about the identities of those killed, from countries including Britain, Australia, New Zealand, the US, Canada, France, China, India, Ghana and the Netherlands.

One of those named was Ross Langdon, an architect with dual Australian-British citizenship. He and his wife, Elif Yavuz, who was due to give birth to their first child in a few weeks, were both killed.

In London the defence secretary, Philip Hammond, has chaired a meeting of the government's Cobra emergency committee. He said Britain was prepared to offer Kenya more help: "We stand ready to provide them with any additional assistance they require. We will be monitoring the situation throughout the day."

Kenya's president, Uhuru Kenyatta, whose nephew and the nephew's fiancée were killed in the attack, has promised to end the siege swiftly: "I assure Kenyans that we have as good a chance to successfully neutralise the terrorists as we can hope for. We will punish the masterminds swiftly and painfully."