There were no immediate reports of people killed in the fighting, although health officials said at least five people had been wounded. NATO forces said in a statement that as many as seven locations were under attack across the capital.
Taliban spokesman Zabiullah Mujahid claimed responsibility for the ongoing assault in a text message to The Associated Press. He said a group of armed suicide bombers launched an attack on the NATO forces headquarters, the parliament building across town and a number of diplomatic residences in Kabul.
More than 10 explosions in all rocked the capital, and heavy gunfire shook the city for more than an hour after the initial blast. Smoke rose over the skyline from a few spots as sirens wailed.
Three other eastern cities also came under attack at about the same time Sunday, but there were few details and the fighting was still going on. The Taliban did not provide any information about attacks outside the capital.
The Kabul attacks began with bombings in the central neighborhood of Wazir Akbar Khan, which is home to a NATO base as well as a number of embassies, including that of the U.S. Gunfire erupted soon after the blasts, forcing people caught out in the street to quickly find cover. Smoke could be seen rising from a few buildings in the neighborhood as sirens wailed.
The American Embassy said in a statement saying that there were attacks "in the vicinity of the US Embassy."
Militants holed up in a tall building were firing rockets in different directions, according to an Associated Press reporter at the scene. It was not immediately clear what they were targeting, but shots appeared to be focusing on the nearby British Embassy.
Britain's Foreign Office in London could not provide details of the attack.
"We can confirm that there is an ongoing incident in the diplomatic area of Kabul," a spokeswoman said on condition of anonymity in line with government policy. "We are in close contact with embassy staff."
At about the same time, residents reported a blast near the parliament building across town. A police officer in the area, Mohammad Assan, said there was an attack involving shooting near parliament.
An official at the parliament, who spoke on condition of anonymity because he was not authorized to speak to the media, said an attacker entered a nearby building and opened fire on parliament and the Afghan Commerce Ministry. The official reported hearing a large blast coming from the building. After that, the gunfire subsided.
On the outskirts of the city, militants also targeted the area around a NATO base known as Camp Warehouse with mortar fire, according to an AP reporter at the scene. Turkish and Greek forces at a nearby Greek-Turkish base were responding with heavy-caliber machine gun fire.
A police officer said a suicide bomber had occupied a building near the bases and was shooting toward the Kabul Military Training Center on Jalalabad road. The officer spoke anonymously because he was not an authorized spokesman.
At least five people were wounded in the violence across the city, said Kabir Amir, head of Kabul hospitals. There were no immediate reports of deaths.
The attacks were the first in the heavily guarded capital since a shooting inside the Interior Ministry in February in which a ministry employee turned a gun on NATO advisers and shot two soldiers dead.
Militants also staged attacks outside Kabul in the capital cities of the provinces of Logar, Paktia and Nangarhar.
In the city of Pul-e-Alam in Logar province, police chief Ghulam Shakhi said militants had entered a building that belongs to the education department, which is near a building used by the Afghan intelligence service, and a gunbattle was under way.
In Paktia province, militants were shooting sporadically from a building across from a university in the city of Gardez, said the deputy provincial police chief Mohammad Zaman. He said Afghan security forces have surrounded the building. The deputy governor, Abdul Rahman Mangal, said they believe two or three suicide bombers are involved in the attack.
NATO said it was aware of reports of an explosion in the proximity of a coalition installation near Jalalabad, the provincial capital of Nangarhar, but could provide no details about the blast.