Nineteen people still missing two days after a Somali militant attack on a Nairobi hotel and office complex that killed 21 people are now accounted for, the Kenyan Red Cross said on Thursday.

Kenyan President Uhuru Kenyatta said on Wednesday evening that a 20-hour siege had ended with security forces killing all the Somali militants who had stormed the hotel complex, forcing hundreds of people into terrifying escapes.

Late on Wednesday, the Red Cross had said it had yet to account for 19 of 94 people it had been tracing. "All 94 cases have been closed positively as of (now)," it said in a statement at 12:30 p.m. (0930 GMT) on Thursday, giving no further detail.

Al Shabaab, a Somalia-based al Qaeda affiliate fighting to impose strict Islamic law, said it carried the assault on the upscale dusitD2 compound over US President Donald Trump's decision to recognise Jerusalem as Israel's capital.

Kenya, the East African hub for multinational companies and the United Nations, became a frequent target for al Shabaab after Kenya sent troops into neighbouring Somalia in 2011 to try to create a buffer zone along its border.

In a two-page statement claiming responsibility for the attack, al Shabaab did not spell out why it had chosen to hit Kenya over Trump's December 2017 decision on Jerusalem.

It said the attack was "a response to the witless remarks of US president, Donald Trump, and his declaration", and that it was targeting "Western and Zionist interests worldwide and in support of our Muslim families in Palestine".

Asked about the claim, a White House National Security Council spokesman said in a statement: "This senseless act is a stark reminder of why the United States remains resolved in our fight to defeat radical Islamist terrorism."

The bloody bodies of five attackers were broadcast across social media as Kenyatta announced the end of the siege, which echoed a 2013 al Shabaab assault that killed 67 people in the Westgate shopping centre in the same district.

Sixteen Kenyans including a policeman, an American survivor of the September 11, 2001 al Qaeda attacks on the United States, and a British development worker were among the dead in the hotel 14 Riverside Drive complex, Nairobi police chief Joseph Boinnet said.