A large explosion was followed by several hours of gunfire. A Nepali guard and an off-duty policeman were killed, along with several militants. A guesthouse used by the International Organization for Migration was hit, and one of their employees badly injured. The Taliban told the BBC it was targeting CIA trainers. Local TV reports said several gunmen were holed up in the area, which is home to a number of institutional buildings and to foreign workers. Kabul police chief Gen Ayub Salangi told the BBC that all but one of five or six assailants had been killed, and that seven policemen were injured.
A Taliban spokesman said the group had targeted CIA trainers instructing Afghans at the National Directorate of Security (NDS) intelligence agency.
The IOM said one of its employees had been badly burned by a grenade attack, and that three security officers had suffered minor injuries.
It was not clear whether the guesthouse was the main target of the attack, which Gen Salangi said had begun with a car bomb.
Some reports said there had been a series blasts as the assault began. Ambulances were shown heading for the scene of the attack.
Smoke was seen over the centre of the city and the blast was felt several kilometres away.
Shopkeepers in the area said the explosion had shattered their windows. Part of Kabul was cordoned off.
The Taliban announced a "spring offensive" in April, saying it would target foreign military bases and diplomatic areas.
Last week another Islamist militant group, Hezb-e-Islami, said it had carried out an attack on a military convoy in Kabul in which at least 15 people were killed and dozens injured.
In the last major attack in Kabul before that, a suicide bomber blew himself up near the defence ministry, killing nine people.
Most international troops are scheduled to leave Afghanistan by the end of 2014. Afghan forces are due to take responsibility for the security of the whole country in the next few months, for the first time since 1992