Gov. Tamim Nuristani said U.S.-led coalition and Afghan forces believed Gulbuddin Hekmatyar was meeting with top deputy Kashmir Khan in the Dohabi district of Nuristan province on Sunday, sparking a fierce bombardment.
Other provincial leaders say many civilians were killed in the hours-long clash, which included airstrikes in the remote villages of Shok and Kendal. Nuristani said it was too early to know if any of the 16 killed were civilians. His casualty figures came from police who had reached the remote district.
U.S. officials and the Afghan Defense Ministry have denied that any civilians were killed.
The competing claims were impossible to reconcile because the fighting took part in a remote and dangerous part of the country. U.S. officials say that militants falsely claim civilian casualties as a strategy to weaken the international military coalition and the Afghan government.
In southern Afghanistan, meanwhile, Taliban fighters attacked and killed seven police eradicating a field of opium poppies in rural Kandahar province, the police chief said. Five militants also died in the clash.
The Afghan Defense Ministry said the battle in Nuristan, a lawless region that borders Pakistan, targeted a terrorist center that included a suicide bomb cell. It said it would release casualty figures later.
Hekmatyar heads the militant group Hezb-i-Islami, which has links with the Taliban and al Qaeda in fighting the Afghan government, though Hekmatyar has denied direct links with those groups.
He briefly served as prime minister of Afghanistan in the mid-1990s and is infamous for bombarding the capital, Kabul, during the country's civil war, killing an untold number of civilians.
The chief of Nuristan's provincial council, Rahmatullah Rashid, said 19 people were killed in the battle - all civilians. He said six children, five women and eight men died. He said he didn't have a report of how many militants were killed. Rashid's information was relayed to him by villagers via radio communications.
U.S. Marine 1st Lt. Richard Ulsh said, "Coalition Forces have received no reports of civilian casualties at this time as a result of that conflict."
Mohammad Farooq, the province's criminal investigations director, said 20 people were killed, including civilians. He said that some two dozen houses were destroyed.
In Kandahar province, meanwhile, seven police were killed during a Taliban attack on a poppy eradication team in Maiwand district, said provincial police chief Sayad Agha Saqib. Five militants also died, he said.
The Afghan government eradicated almost 40,000 acres of poppies last year, but the country's farmers still grew 477,000 acres of poppies, a record haul. Attacks on poppy eradication teams are common.
Afghanistan last year produced 93 percent of the world's opium, the main ingredient in heroin.
In nearby Helmand province, two police were killed when they hit a roadside bomb while escorting engineers to repair a mobile phone tower Monday in Sangin district, said provincial police chief Mohammad Hussein Andiwal.
"The Taliban don't want mobile phone towers," Andiwal said.
At least 10 mobile phone towers have been attacked in the last month following a warning by the Taliban to shut down the towers at night. Taliban fighters fear they are being tracked by the U.S. and NATO militaries by signals from their mobile phones. In response, phone companies have curtailed service at night throughout the south.