Security forces are seen at the scene of a blast in Nairobi, Tuesday, Jan. 15, 2019. An upscale hotel complex in Kenya's capital came under attack on Tuesday, with a blast and heavy gunfire. (AP Photo/Ben Curtis)

Nairobi - Armed assailants involved in the terrorist attack on a hotel in Nairobi are still in the building, police said on Tuesday, adding that there had been injuries.

"A group of armed assailants attacked the Dusit (Hotel) complex in a suspected terror attack," Kenyan police chief Joseph Boinnet said in a statement.

"We are aware that armed criminals are holding up inside the hotel and specialist forces are now currently flushing them out," he added.

There had been injuries, he said, but gave no details. According to earlier reports, three people have been killed in the attack. 

Television footage showed members of the bomb squad outside the hotel, smoke coming from buildings, and ambulances arriving at the scene.

"Our people are still on the ground, we shall communicate when we have information," Kenyan Red Cross spokesperson Noellah Musundi told dpa by phone, refusing to confirm whether there were deaths.

The United States embassy in Kenya issued a security alert for its citizens, advising them to stay away from the area.

Al-Shabaab, a jihadist group which regularly launches attacks in Somalia and neighbouring Kenya, meanwhile, claimed responsibility on its Radio Andalus.

"Our brave Mujaahideens are engaging in ongoing fighting inside Nairobi against the infidels ... The attack started with a bombing," they said.

The Al-Qaeda-linked militant group is fighting to topple the country's government and establish an Islamist state based on its strict interpretation of Islamic law.

Al-Shabaab often targets hotels popular with diplomats, foreigners and senior officials in Somalia too, as well as government offices.

In 2013, in one of the worst terrorist incidents in the Kenyan capital, at least 67 people were killed in an attack on the Westgate Mall, also claimed by Al-Shabaab.

The attack at the Dusit comes on the third anniversary of an attack on a Kenyan military base in which almost 200 soldiers were killed.