Kenyan authorities say a third terrorist has been killed by security forces attempting to take control of the Westgate mall in Nairobi.
The police and army say they now control all of the building’s four floors.
Eleven soldiers have been injured in the latest assault.
Though most of the hostages had been freed, several gunmen remained on the loose inside the building, possibly holding hostages.
The Kenya Red Cross and the Interior Ministry said 62 people, among them a number of foreigners, were killed and at least 175 injured during the three-day siege. The death toll could rise further, officials have cautioned.
The Somali Islamist militia al Shabaab has claimed responsibility for the attack.
Loud explosions and sustained gunfire were heard several times during the day as Kenyan security forces moved in on al Qaeda-linked gunmen.
Authorities said the attackers set fires inside the building as they were being cornered. While the government pledged it would extinguish the flames, it appeared firefighters were still unable to access the building.
“We can confirm that almost all of the hostages have been evacuated,” said Interior Minister Ole Lenku. He declined to give precise numbers.
“We are fully in control of the situation,” he added.
Lenku said two attackers were killed and several injured as the military-led assault was taking place to free hostages.
General Julius Karange, head of the Kenya Defence Forces, said the attack was staged by a “multinational” group of attackers.
Finland’s interior minister, Paivi Rasanen, has said his country is investigating reports that a Finnish national might have been part of the attack. Unconfirmed reports had earlier suggested that Americans and Britons might also have been involved in the worst terrorist attack in Kenya since a bomb attack on the US embassy 15 years ago.
Government authorities have been saying since Sunday that the siege is about to end.
Soldiers, police and special units, including snipers, were positioned around the four-storey building, backed up by helicopters. Elite troops could be seen moving around the area.
The Red Cross said 63 people were still listed as missing.
The governments of Canada, France, Britain, South Africa, the Netherlands and the United States said some of their citizens had been killed or injured in the massacre.
Kenyan Tourism Minister Phyllis Jepkosgei Kandie sought to assure tourists – a vital source of revenue for the country – that they should not cancel their visits.
“We want to assure our international visitors and tourists not to panic and continue with your activities,” she said in remarks broadcast on local KTN television.
“We assure you that you are safe wherever you are,” she added.
Some 10 to 15 attackers from al-Shabaab were cornered in one part of the building with the hostages when security forces launched a “major assault” late Sunday.
Security forces are believed to be sharing information with foreign security agencies, as they try to find a way to fully regain control over the shopping centre.
British Prime Minister David Cameron cut short his annual visit to Queen Elizabeth II at her home in Balmoral, Scotland to chair a meeting of the emergency committee Cobra to help with the crisis.
Israel’s deputy ambassador to Nairobi, Yaki Lopez, said his country was helping Kenya.
“We are on the ground. We are providing help,” he told the Israeli Ynet news website, giving no further details.
The mall, a popular shopping spot for expatriates and locals, has been cordoned off and security has been beefed up across Nairobi.
Kenyan medics have been calling for blood donations, with a steady stream of volunteers lining up at various locations in the capital and elsewhere in the East African nation.
Al-Shabaab said the attack was in response to Kenya’s military presence in southern Somalia. The group has pledged large-scale attacks against Kenya for over two years.
The government sent troops to Somalia in 2011 to fight an insurgency and prevent cross-border raids following a spate of kidnappings by al-Shabaab on Kenyan soil.
The Islamist group, which has threatened to kill hostages, is demanding that Kenya withdraw from Somalia for them to end the siege.
The mall lies in Westlands, a wealthy Nairobi neighbourhood where United Nations workers and diplomats reside.
Meanwhile, in The Hague, Kenya’s Deputy President William Ruto was given permission by the International Criminal Court (ICC) to return home for a week to help deal with crisis.