Abdul Hamid, a provincial border police regiment commander, said the bomb on Thursday struck a patrol near the border with Pakistan in eastern Paktika province.
"They came under US bombardment and 12 policemen were killed, including the police commander," he said.
The US-led multinational force, which has been searching for Taliban fighters in the province, had apparently come under earlier attack, he said.
"They may have mistaken our convoy for the enemy."
Colonel Thomas Collins, a multinational force spokesperson, said the event was under investigation.
"We are scrambling to get the details," he said.
Hamid Karzai, the president of Afghanistan, said he was "shocked and angered" and had ordered his own investigation.
The bombing is the latest in a string of coalition bombings that have killed civilians or Afghan security forces.
"I have repeatedly asked the coalition forces to take maximum caution while carrying out operations and I want that incidents like this must not be repeated," Karzai said in a statement which put the death toll at 10.
In another incident, 15 health workers, mainly doctors and nurses, kidnapped in a Taliban stronghold in southern Afghanistan early on Thursday, were freed unharmed hours later, a government official said.
A man purporting to be a Taliban commander said his men had captured and then decided to release the 15, who were snatched in Kandahar province as they were on a mission to a refugee camp in Zhela district.
Qari Yousuf, another purported Taliban leader, said that his group's members had not taken the medics but had taken the group's minivan and left the team to flee to nearby villages.
Provincial refugee department official Agha Jan Nazari told AFP: "All 15 health workers are back in Kandahar [city].
"They are in good condition. They all came back in the afternoon."
Nazari confirmed that the bus in which they were travelling had not been returned.
Also in Kandahar province, a bomber detonated an explosives-laden van near a Nato and Afghan military convoy on Thursday morning.
One Nato soldier was wounded in the attack, officials and witness said.
In a separate incident, another suicide bomber attacked an Afghan police post in the southern province of Uruzgan, killing himself and wounding seven policemen.
Karzai says such incidents should
not be repeated
The man was being chased by Afghan security forces when he ran into the police post and detonated his bomb, said Mohammad Qasim, Uruzgan police chief said.
"We had information in advance of a suicide attack and we were chasing him," Qasim said.
Three of the injured policemen were critically injured in the attack.
The Taliban spokesman, Qari Yousuf, took credit for the attack and said that the bomber was an Afghan.
Amruallah Saleh, Afghanistan's director-general of intelligence, has also said his country would struggle to defeat the Islamist insurgency without more co-operation from Pakistan.
Saleh told Afghan parliament's lower house on Thursday that the Islamist insurgents depended on training facilities and organisational centres in neighbouring Pakistan.
"Pakistan has not given up its interference and aggression," Saleh said.
Saleh conceded there were shortcomings in the Afghan government, but said the source of insecurity lay on the other side of the Durand Line dividing Afghanistan from Pakistan.
"As long as the war against terrorism is not extended openly and seriously from Afghanistan, we cannot restore full security in our country.
"The enemy's organisation set-up, the enemy's financial resources, the enemy's training sites and all it has, lie on the other side of the Durand Line where our arms can't reach."