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.
Kenyan police chief Joseph Boinnet said the attack began about 3pm on Tuesday with an explosion targeting cars outside a bank followed by a detonation from a suicide bomber in the hotel lobby. As he spoke, a Reuters reporter on the scene reported heavy gunfire, then an explosion shortly afterwards.
Surveillance video showed three attackers dressed in black running across the car park at 3.30pm shortly followed by a fourth. At least two of the men were wearing green scarves in the close-up footage. One appeared to be wearing a green belt with grenades.
Two Kenyans in their early 30s working with governance consultants Adam Smith International were among the dead, a family member said. Both had young families, she said.
A Spanish national was among the injured, a Spanish diplomat told Reuters.
The US Embassy had offered assistance, a State Department official said, adding all American diplomats were safe.
A woman shot in the leg was carried out of the complex, and several men emerged covered in blood. Some office workers climbed out of windows. Many told Reuters they had to leave colleagues behind, still huddled under their desks.
"There's a grenade in the bathroom," one officer yelled as police rushed out from one building.
Geoffrey Otieno, who works at a beauty salon in the complex, said he heard a loud bang from something thrown inside the building, then saw shattered glass.
"We hid until we were rescued," he said.
Meanwhile, Simon Crump, an Australian who works for an international firm in the complex, barricaded himself inside a spare room with two other people. They waited there for about two and a-half hours for help to arrive, their minds racing.
"You’re hiding under a desk trying to figure out what’s going on, and you just don’t know, as there’s so much misinformation," he said.
When soldiers finally reached the group, they instructed them to put their phones away and put their hands in the air as they made their way to safety.
Al Shabaab, which wants to overthrow the weak, United Nations-backed Somali government and impose strict Islamic law, quickly said it was responsible.
"We are behind the attack in Nairobi. The operation is going on," Abdiasis Abu Musab, the group's military operations spokesman, told Reuters by telephone in Somalia.
According to its website, 14 Riverside is home to local offices of international companies including Colgate Palmolive, Reckitt Benckiser, Pernod Ricard, Dow Chemical and SAP, as well as the dusitD2 hotel, part of Thai group Dusit Thani.
Kenya is a base for hundreds of diplomats, aid workers, businessmen and others operating around East Africa.
The Australian Embassy is across the road from the compound.
"I just started hearing gunshots, and then started seeing people running away raising their hands up and some were entering the bank to hide for their lives," a woman working in a bank in the complex said, adding she heard two explosions.
Kenyan television featured appeals for blood from local hospitals and showed police cordoning off the route to ensure vehicles could move quickly. Red Cross ambulances ferried victims away.
Kenyan troops, concentrated in southern Somalia, originally entered the country to try to create a buffer zone along the shared border. They now form part of an African Union peacekeeping force.
The attack took place as a Kenyan court prepares to sentence four men accused of aiding the Westgate mall attack.
