Kenya's president said early on Wednesday that security forces had killed all four militants who stormed an upscale hotel complex in Nairobi the previous day, in an attack that killed at least 14 people.

Uhuru Kenyatta said 14 civilians were confirmed dead and over 700 others had been safely evacuated.

The attack on the dusitD2 hotel began shortly after 3pm on Tuesday with an explosion in the parking lot and then a suicide bomb blast in the foyer, police said.

Somali militant Islamist group al Shabaab claimed responsibility for the attack.

At least two groups of people had still been trapped inside as dawn broke, and gunfire continued to ring out around the complex in Riverside Drive.

An earlier estimate put the death toll at 15.

Eleven Kenyans, an American and a Briton were among the casualties, morgue staff said. Two victims had not been identified.