At least one policeman and two attackers have been killed in gun battles between security forces and insurgents in the city.
A Western military official confirmed Nato's International Security Assistance Force, ISAF, headquarters was one of the targets under attack.
The US embassy could not confirm that its compound was under attack but said staff had been ordered to take cover.
Up to six insurgents are reported to have launched a coordinated assault in the early afternoon in the heavily protected heart of the Afghan capital.
Afghan officials said two separate suicide attacks targeted police, one near parliament. Three policemen were wounded in those attacks, the interior ministry said. Both were in the western part of the capital.
The ISAF headquarters in Kabul oversees the operations of the bulk of the estimated 140,000 foreign troops fighting the Taliban in Afghanistan.
Officially Kabul is under the control of Afghan security forces, along with most of its surrounding province and six other parts of the country handed over by Nato-led troops in July as part of a staggered, timetabled withdrawal.
This year has proved the bloodiest so far since US-led forces ousted the Taliban in 2001.