The strikes, which come a day after Taliban fighters stormed a NATO base in eastern Afghanistan, show the insurgents' fighting spirit has not been broken despite a surge of U.S. troops and firepower.
Also Sunday, the Afghan president's office said the former ambassador-designate to Pakistan, who was seized by gunmen two years ago in the Pakistani city of Peshawar, has been released and is back home safe.
CBS News Complete Coverage: Afghanistan
The diplomat, Abdul Khaliq Farahi, was freed in eastern Afghanistan late Saturday in a joint effort by officials from both countries and has returned to Kabul, where he met Sunday with President Hamid Karzai, the Afghan leader's office said. A brief statement gave no details on how he was freed.
Farahi was heading from the Afghan consulate toward his home in the border city of Peshawar on Sept. 22, 2008, when gunmen stopped the vehicle and killed his driver.
"Abdul Khaliq Farahi is in good condition and right now he is in Kabul with his family," Karzai's office said.
NATO said three coalition service members were killed in an insurgent attack in eastern Afghanistan. The international military coalition did not provide further details or the nationalities of the dead service members.
In the south, a roadside bomb killed a Danish soldier and wounded an interpreter, Denmark's military said. The are some 700 Danish troops in Afghanistan, based mainly in Helmand province. A British soldier was also killed Sunday while on patrol in Helmand, Britain's Defense Ministry said.
Sunday's deaths brought to 31 the number of coalition service members who have died in Afghanistan so far this month.
Insurgents also killed three Afghan policemen, who died when their vehicle hit a roadside bomb in Uruzgan province in the south, said Gov. Khudi Rahim. Two other policemen were wounded in the blast in Tarin Kot district, he said.
Tens of thousands of Afghan and coalition troops are pressing insurgents throughout southern and eastern Afghanistan, and militants are retaliating with attacks on government workers and others aligned with the international troops.
A bomb attached to a motorcycle exploded in a marketplace in the Spin Boldak district of Kandahar province, just east of the Pakistan border, killing two people and wounding 10, said district government chief Abdul Ghani.
Also in Nangahar province, a bomb placed in a wheelbarrow exploded in the provincial capital of Jalalabad, killing one person and wounding nine others, including six children and two women, the Interior Ministry said.
Insurgents also set fire to a NATO fuel convoy early Saturday morning. A group of gunmen rushed the trucks in Behsud district of Nangarhar province the same area on the edge of Jalalabad city where a group of would-be suicide bombers tried to storm a NATO base on Saturday, provincial government spokesman Ahmad Zia Abdulzai said.
The truck drivers quickly fled and the insurgents set 12 tankers ablaze, said Abdulzai. Firefighters worked to quell the flames throughout the morning, as police secured the area. No one was killed in the attack, Abdulzai said.
Insurgents on both sides of the Afghan-Pakistan border have routinely struck NATO supply convoys including a pair of attacks on Oct. 6 in which 55 fuel tankers were set ablaze in Pakistan. The alliance says the attacks have not caused supply problems for troops.
NATO also reported that it was investigating the death of an Afghan child, who was inadvertently killed during fighting Sunday in Zhari district of Kandahar province. Another child also was wounded when Afghan and coalition forces shot back after coming under fire from insurgents, the coalition said.