The attack emphasized the insurgency's continued ability to wreak violence despite fierce efforts by the Afghan government and international forces to wipe out their leadership.
In Kunar, two attackers wearing suicide vests detonated their explosives as a NATO foot patrol passed by the headquarters of the provincial government, provincial police chief Ewas Mohammad Naziri said.
NATO confirmed that three of its service members were killed in a suicide attack, but did not give any more details, including the nationalities of the troops who were killed. Wednesday's attack brought to 15 the number of international troops killed so far in August.
At least one Afghan civilian was killed and three were wounded in twin blasts that took place at about 10 a.m., said Wasifullah Wasify, a spokesman for Kunar's governor.
He said the bombers struck just outside the government compound in the provincial capital of Asadabad during a meeting of the provincial council. Several foreigners were also in the compound, attending a security briefing.
Taliban spokesman Zabiullah Mujahid said in a statement that two insurgents drove explosives-laden vehicles into the NATO patrol from opposite directions. He claimed they killed 17 international soldiers. The insurgents typically claim far higher death tolls in their attacks.
The other attack later on Wednesday took place when a roadside bomb hit a bus in the western province of Farah, killing at least three people, a passenger said. Many of the wounded were unable to get help because of an ongoing battle between insurgents and Afghan police, police and the local health director said.
Insurgents attacked a police checkpoint in Farah province around midday Wednesday, and the struggle for the road continued for hours, provincial deputy police chief Mohammad Ghaws Milyar said. He said one militant was killed but police casualties were still unclear because the battle was still ongoing in the late afternoon.
The bus, which had been traveling in the same area, hit a roadside bomb apparently planted by insurgents, but Milyar said police were unable to determine how many had been killed or to help the wounded because of the fighting.
The health director of Farah province, Abdul Jabar Shayuq, said two wounded civilians and one dead body were ferried to a local hospital. He said the wounded told him that many more people were trapped on the bus.
One of the wounded men spoke to The Associated Press by telephone from the hospital. Abdullah, 52, said his wife was killed by the explosion. He said he had counted at least two more bodies before a villager passing by in a car picked up him, his wounded son and one of the bodies, taking them all to the hospital.
Abdullah was wounded by shrapnel in the forehead and the shoulder. He said the body of his wife was still at the scene along with several wounded people.
"They were shouting for help, but nobody was there to help them," said Abdullah, who like many Afghans uses just one name. He added that the car he escaped in had no more room and ambulances could not reach the bus because of fighting.
It was unclear by late Wednesday if the battle had ended or if the bus passengers had been rescued.