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A police officer said a suicide bomber had occupied a building near the bases and was shooting toward the Kabul Military Training Center there. 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.

Sediq Sediqi, a spokesman for the Interior Ministry, said two suicide attackers have been killed — one who was firing from a building under construction behind the Kabul Star Hotel and one in a building under construction near the parliament.

The coordinated assaults showed a sophistication that is reminiscent of the last sustained attack in the heavily guarded capital in September 2011.

In that strike, six fighters with heavy weapons took over an unfinished high-rise and fired on the U.S. Embassy and NATO headquarters about 300 yards away. They then held out against a 20-hour barrage by hundreds of Afghan and foreign forces.

By the time the fighting ended, insurgents had killed 16 Afghans — five police officers and 11 civilians, more than half of them children. Six or seven rockets hit inside the embassy compound, but no embassy or NATO staff members were hurt.

Fighting was also continuing Sunday in the provincial assaults in Jalalabad city, Logar province and Paktia.

“In Jalalabad city, four attackers were killed,” Mr. Sediqi, the Afghan Interior Ministry spokesman, said. “In Logar province, the attack is still going on, and the area is surrounded by police. In Paktia, the area has been surrounded by police, but a gun battle continues.”

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.

In Jalalabad, the capital of Nangarhar province, would-be suicide bombers launched separate attacks on the military airfield used by NATO and Afghan forces and a smaller NATO base nearby. Four attackers wearing suicide vests tried to storm the entrance to the airfield in a vehicle but were fought off by NATO forces. Three were killed and one escaped, said Amir Khan Lewal, deputy provincial police chief.

At the nearby base, two attackers were shot dead before they could breach the bases defenses, but there was also an explosion inside the base, Chief Lewal said. It was not immediately possible to reconcile his figures with those of the Interior Ministry.

NATO said it was aware of reports of an explosion in the proximity of a coalition installation near Jalalabad but could provide no details about the blast.

Associated Press writers Deb Riechmann and Amir Shah contributed to this report.