Taliban fighters launched concerted attacks on several embassies - including the British, German and Russian missions - in the diplomatic enclave of Kabul, local media reported.
The insurgents, using rocket-propelled grenades, also targeted Nato headquarters and the parliament building.
"We claim responsibility for these attacks," Reuters reported Taliban spokesman Zabinullah Mujahid as saying.
"A group of armed suicide bombers have launched an attack on NATO forces headquarters, parliament and a number of diplomatic residences in Kabul," read a text message from Mujahid to the Associated Press.
Unconfirmed reports also said gunmen tried to enter the parliament and were driven out by Afghan forces.
The security forces are said to be scrambling to bring back order in the city.
"ANSF and ISAF responding as needed," a spokesman for NATO's International Security Assistance Force tweeted, according to Reuters.
Insurgents also targeted a hotel complex near the presidential palace and the Iranian Embassy, according to Afghan media. And rockets were also landed at a supermarket near the German Embassy that is frequented by the foreigners.
Casualty figures were unknown. The cities of Jalalabad and Gardez also were reportedly attacked.
At least seven explosions were heard in the heavily guarded diplomatic zone of central Kabul. Heavy gunfire followed for more than 30 minutes in the Wazir Akbar Khan district of central Kabul as the residents ran for cover.
Some other reports also suggest smoke coming out from several important buildings.
In a separate incident, Taliban men stormed a jail in northwest Pakistan on Sunday morning and freed 400 prisoners including Taliban militants.