Gunmen have stormed an upscale hotel and office complex in the Kenyan capital, setting off loud blasts and sending people fleeing for their lives following a coordinated assault claimed by the Somalia-based al-Shabab armed group.

More than 16 hours after the attack began at Nairobi's Dusit hotel complex - which also includes bars, restaurants, offices and banks - bursts of gunfire and explosions were still heard in the area despite earlier government assurances that everything was under control.

At 7am (04:00 GMT) on Wednesday heavy gunfire rang out again.

"We still believe there are two or three attackers in specific locations," an unidentified police officer told AFP news agency. "The situation is far from over."

It was unclear how many people were still trapped inside. A group of about 150 workers was escorted from a building where they had sought refuge. Many more remained inside and some needed first aid for gunshot wounds, a first responder told the Reuters news agency.

Kenya's Interior Minister Fred Matiang'i had said at 11pm that all buildings at the scene had been secured and scores of people evacuated. But he did not comment on the attackers' whereabouts and said security forces were still "mopping up".

By 1am local time, 15 bodies arrived at Chiromo Mortuary and more were expected. Identification papers indicated 11 were Kenyan, one was from the United States and one from Britain, he said. The other two were not carrying documents.

A Kenyan police officer, who spoke on condition of anonymity, was quoted by The Associated Press as saying 15 bodies were taken to the morgue.

The US State Department confirmed a US citizen was among those killed, but did not release the identity of the victim.

Al-Shabab, which has been fighting the Western-backed government in Somalia, claimed responsibility for the attack, saying on Tuesday it was in control of most parts of the building complex.

"Our fighters killed 47 enemies inside the complex. The mujahideen are still in control of most parts of the building complex," Abdiaziz Abu Mus'ab, the group's military operations spokesperson, told Al Jazeera.

Authorities did not comment on the number of the attackers but Kenya's Citizen TV aired security-camera footage that showed at least four heavily armed men in dark-coloured, paramilitary-style gear.

No casualty figures have been released by officials, but witnesses reported seeing several bodies.

A police officer who spoke on condition of anonymity because he was not authorised to talk to reporters said bodies were seen in restaurants downstairs and in offices upstairs, but "there was no time to count the dead".

A witness who gave his name only as Ken said he saw five bodies at the hotel entrance. Other people were shouting for help and "when we rushed back to try to rescue them, gunshots started coming from upstairs, and we had to duck because they were targeting us and we could see two guys shooting", he told the AP.

'What I have seen is terrible'

The coordinated assault began with an explosion that targeted three vehicles outside a bank, and a suicide bombing in the hotel lobby that severely wounded a number of guests, Joseph Boinnet, Kenya's national police chief, said in a televised statement.

Survivors reported hearing a shattering blast and saw people mowed down by attackers as they sat in a cafe. Victims were left slumped on tables.

"We were changing our shifts, and that is when I heard a loud blast and people were screaming," said Enoch Kibet, who works as a cleaner at the cafe and managed to crawl out a basement gate. "I couldn't believe I was alive. The blast was so loud and shook the whole complex."

"The main door of the hotel was blown open and there was a human arm in the street severed from the shoulder," said Serge Medic, the Swiss owner of a security company who ran to the scene to help when he heard of the attack from his taxi driver.

"It is terrible. What I have seen is terrible. I have seen a human as I ran out and there is what looks like minced meat all over," said a man who ran from the scene. He did not elaborate further.

Hospitals appealed for blood donations even as the number of wounded remained unclear. Kenyan television showed police cordoning off the route to ensure vehicles could move quickly. Red Cross ambulances ferried victims away.

The attack came a day after a trial began in the 2013 Westgate mall attack case. At least 67 people were in killed in that attack, which was also carried out by al-Shabab.

Kenyan prosecutors say suspects in the Westgate case currently on trial committed a terrorist act and used false documents. The men deny all charges.

The African Union chief, Moussa Faki, condemned the attack and commended Kenyan security forces for their "swift response".

UN Secretary-General Antonio Guterres also denounced "the horrible terrorist act".

Spate of attacks

The East African country faced a spate of attacks after it sent its army into Somalia in 2011 to fight the al-Qaeda-linked group.

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Kenyan troops, concentrated in south Somalia, originally went into Somalia to try to create a buffer zone along the border. They are now part of an African Union peacekeeping force.

Tuesday's attack came exactly three years after al-Shabab overran a Kenyan army base in Somalia, killing dozens of soldiers.

On April 2, 2015, in one of the most gruesome attacks on Kenyan soil, the armed group killed 148 people, most of them students, at a university in Garissa, eastern Kenya.