The heavily guarded area of Kabul where the attacks took place is frequented by foreigners and is rarely the scene of violence. The fighting was still on late Sunday evening.
Afghan government facilities were also targeted, the NATO's International Security Assistance Force said. The Taliban claimed responsibility for the attacks, saying its suicide bombers were carrying them out in Kabul and and three provinces around the country, CNN reported.
Afghan policemen at the scene of attacks. Photo: AFP
The Islamist militia that once ruled Afghanistan said its fighters attacked the parliament building and other sites. The attackers had suicide vests, RPGs, and grenades, it said.
The US embassy went into lockdown, with spokesman Gavin Sundwall describing it the "standard operating procedure". All staff were "accounted for and safe", and the embassy had no reports of injuries to its personnel, CNN quoted Sundwall as saying.
India said it was in constant touch with its embassy in Kabul and its citizens living in that country were safe.
"We are in constant touch with our embassy in Kabul. All Indian citizens are reported to be safe," said a statement issued by the external affairs ministry in New Delhi.
Britain's foreign office said there was an "ongoing incident in the diplomatic area of Kabul. We are in close contact with embassy staff".
The ISAF said it had no confirmed reports of casualties in Kabul.
A police officer said attackers took over a Kabul hotel close to the presidential palace, UN office and foreign embassies, but staff there denied it had been attacked.
Three insurgents were killed near the Kabul Star Hotel, and there was a standoff at a building in the neighborhood, interior ministry spokesman Sadiq Saddqui said on Afghan TV.
Earlier, Xinhua reported that blasts and gun shots were heard inside the hotel after militants stormed the building. It reported that some suicide bombers had entered the building.
Meanwhile, in the east of the country, four suicide bombers tried to attack the Jalalabad airfield where US troops are based, the airfield commander said.
One of the attackers blew himself up, while police intercepted the other three. The Taliban claimed responsibility for the attacks in a text message to CNN and on Twitter.
"Several suicide bombers launched attacks around different parts of Kabul, including ISAF/NATO headquarters, Afghan parliament building, and the whole of the diplomatic quarter. The fighting is still ongoing and so far there has been a large loss of the enemy," CNN quoted the Islamist militia as saying.