In what can be described as a swift response, Kenya president, Uhuru Kenyatta, says all gunmen who attacked a luxury hotel in Nairobi have been killed by security forces.

The attack on DusitD2 hotel complex, which includes bars, restaurants, offices and banks led to the death of 14 people on Tuesday.

"All the terrorists have been eliminated," President Uhuru Kenyatta said on Wednesday when announcing an end to the operation to secure the complex in the capital, Nairobi.

In a televised address, Kenyatta did not say how many attackers were involved. He said more than 700 people were evacuated during the security operation and he urged Kenyans to "go back to work without fear," saying the East African country is safe for citizens and visitors.

Hours before Kenyatta spoke, sporadic gunfire could be heard from the scene after scores of people were rescued at daybreak during what police called a mopping-up exercise.

The attack involved at least four armed men who invaded the hotel and shops.

Al-Shabab — the Somalia-based extremist group that is allied to al-Qaida — claimed responsibility for the carnage at the DusitD2 hotel complex, which includes bars, restaurants, offices and banks and is in Nairobi's well-to-do Westlands neighbourhood with many foreign expatriates.

Al-Shabab carried out the 2013 attack at the nearby Westgate Mall in Nairobi that killed 67 people.

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The U.S. State Department confirmed that an American citizen was among those killed, but did not release the victim's identity.

Authorities sent special forces into the hotel to flush out the gunmen. Early on Wednesday, Kenya's Interior Ministry said in a tweet that all buildings had been secured and there was no further threat. At dawn, another explosion and gunfire were heard.

"To God be the Glory. We have been rescued. Over 50 people in my group. No injuries," tweeted a Kenyan businesswoman, Aggie Asiimwe Konde.

Kenya's Citizen TV aired security-camera footage that showed at least four heavily armed men in dark-colored, paramilitary-style gear.

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, said Kenya's national police chief, Joseph Boinnet.

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