The attack unfolded at 3pm local time (12pm GMT) on Tuesday. Terrified people were forced to hide under desks to escape as security forces fought gun battles with militant fighters. A British man and an American man are among the casualties, a mortuary worker said.
The fundamentalist group al Shabaab have claimed responsibility for the attack.
Gunmen allegedly from the militant group set off thunderous explosives and opened fire at people sitting at cafe tables and desks.
A total of 11 of the other victims are believed to be Kenyan.
The nationalities of the others is not yet clear.
Scores of people have been evacuated from the scene of the carnage, Kenya’s interior minister said late on Tuesday evening.
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But the whereabouts of the attackers is still unknown and security forces are still “mopping up”, the official said.
The savage attack occurred at the DusitD2 complex in Nairobi, the African nation’s capital.
The complex, which comprises bars, restaurants, offices and banks, is popular with US, European and Indian ex-pats.
There was little victims could do but hide in terror as militants entered the compound and detonated a series of devices.
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They sprayed the hotel with gunfire as panicked guests hid in their rooms.
Video footage shows terrified people leaving the scene with their hands raised as blazes rage inside nearby vehicles.
Authorities have confirmed they do not know how many attackers there were – but CCTV images appeared to show at least four different terrorists were involved.
More footage from inside the hotel showed Kenyan security officers scouring the building.
A woman working in a neighbouring building said: “I just started hearing gunshots, and then started seeing people running away raising their hands up and some were entering the bank to hide for their lives.”
One officer told the BBC: “Things are not good. People are dying.”
Hotel cleaner Enoch Kibet, who escaped by crawling out of a gate in the basement, told Sky News: “People were screaming. I couldn’t believe I was alive. The blast was so loud and shook the whole complex.”