Heavy gunfire could be heard as Kenyan security officials said they were attempting to kill or capture the remaining attackers and end the nearly 24-hour-long bloodbath at the Westgate mall.
Somalia's Al Qaeda-inspired Shebab rebels said the carnage at the part Israeli-owned complex was in retaliation for Kenya's military intervention in Somalia, where African Union troops are battling the Islamists.
"Let me make it clear. We shall hunt down the perpetrators wherever they run to. We shall get them. We shall punish them for this heinous crime," he vowed.
Two Indians and a South Korean were among the dead. Paris confirmed that two French citizens were among those killed in what it condemned as a "cowardly" attack. Canada's Prime Minister Stephen Harper said two Canadians, one of them a diplomat, were among the dead, while official Chinese news agency Xinhua said one Chinese woman was killed.
Security agencies have long feared that the shopping centre could be targeted by Al Qaeda-linked groups.
The attack was the worst in Nairobi since an Al-Qaeda bombing at the US embassy killed more than 200 in 1998.
After a day and night of sometimes ferocious gun battles, security sources said police and soldiers had finally "pinned down" the gunmen. The Kenyan Red Cross appealed for blood donations and authorities urged residents to steer clear of the area.
"We still do not know the number of hostages nor the attackers but we hope to bring this to an end today," he said.
"The gunmen tried to fire at my head but missed. I saw at least 50 people shot," mall employee Sudjar Singh said.
