The death toll in a Taliban attack on a Kabul restaurant popular with foreigners and affluent Afghans has risen to 21, the deadliest violence against foreign civilians in the country since the start of the war nearly 13 years ago.

Kabul police chief General Mohammad Zahir Zahir said that the victims included 13 foreigners and eight Afghans, and that the majority are civilians.

He said the three attackers, including a suicide bomber and two gunmen, were also killed during Friday's assault on the Lebanese restaurant.

The dead included the head of the International Monetary Fund in Afghanistan and three United Nations staff.

The Taliban claimed responsibility for the attack. Insurgents have frequently targeted foreign interests around the country and in Kabul.

The Foreign Office said a British national was among those killed.

The assault began with the suicide bomber detonating his explosives at the front door of the restaurant, in an area housing several embassies, non-governmental organisations and the homes and offices of Afghan officials.

As chaos ensued, the two other attackers entered through the kitchen and began shooting. They were later killed by security guards.

The US condemned "this despicable act of terrorism in the strongest possible terms", State Department spokeswoman Jen Psaki said.

The restaurant, like most places frequented by foreign diplomats, aid workers, journalists and businessmen in the war-weary country, has no signs indicating its location and is heavily secured. It is on a small side street in the diplomatic quarter of the central Wazir Akbar Khan area, just off a bumpy semi-paved road in a house with low ceilings and an enclosed patio, but no windows.

Bags of dirt are piled up around it to act as blast walls, and guests must go through a series of steel airlocks, where they are searched before entering. The surrounding area is full of police and security guards to protect against insurgent attacks, which have increased in recent months around the country.

Taliban spokesman Zabihullah Mujahid said the attack targeted foreign officials dining at what he described as a "hotel".

"There was a suicide attack on a foreign hotel where special foreign invaders are coming for dinner. In this attack an explosive was used which was very strong and heavy casualties and massive destruction happened," he said.

Zabihullah said the targets of the attack included "high-ranking German officials" and the German foreign ministry said it was investigating. The Taliban frequently provide exaggerated casualty figures.

Insurgents have frequently targeted foreign interests around the country and in Kabul. The Taliban has increased attacks in recent months after foreign forces handed over control of security for the country to the Afghan army and police. Foreign forces are due to withdraw from the country altogether by the end of this year.

A security agreement that would keep about 10,000 US troops and about 6,000 from allied nations past 2014 has been delayed by President Hamid Karzai's refusal to sign it until Afghans elect his successor in the April 5 election.

The deal is seen as crucial to train and mentor the nascent Afghan security forces, which now number about 350,000. If the deal falls through, the US has said it will pull all its forces out of Afghanistan.

International officials said the dead included two Britons, two Canadians, a Dane, a Russian, two Lebanese, a Somali-American and a Pakistani. At least four people were wounded and about eight Afghans, mostly the kitchen staff, survived.

Five women, four foreign and one Afghan, were also among the dead, Gen Zahir said.

The dead included the head of the IMF in Afghanistan, Wabel Abdallah, a 60-year-old Lebanese national; a Danish European Policewoman and her British bodyguard, while the UN in Kabul said its three staff members included a Pakistani, a Russian and a Somali-American. The restaurant's Lebanese owner, Kamal Hamade, was also killed.

The attack was condemned by the UN Security Council, Nato and the European Union.

"I strongly condemn this attack on random civilians and my thoughts and deepest sympathy goes to the next of kin," Danish prime minister Helle Thorning-Schmidt said in a statement.

The Danish foreign ministry refused to release details about the victim but Denmark's TV2 said she was a 34-year-old woman.

"I condemn in the strongest possible terms this appalling and unjustifiable violence. The perpetrators must be brought to justice," EU High Representative Catherine Ashton said.

Afghan president Hamid Karzai's office has not yet condemned the attack.