The Taleban say Afghan officials have handed over to them the body of former senior commander Mullah Dadullah in exchange for the release of hostages.
Mullah Dadullah is the most senior militant to be killed in recent years
Dadullah, who was killed last month in a battle, has been reburied in southern Kandahar province, the Taleban said.
Four hostages held by the Taleban have been freed, Afghan officials confirm. There is no news of a fifth hostage.
A Taleban spokesman said earlier the man was killed because the government delayed handing over Dadullah's body.
There was no immediate comment on the Taleban claim from the authorities.
The BBC's Charles Haviland in Kabul says government figures have tended to distance themselves from any link between the two issues.
Mullah Dadullah was one of the Taleban's most brutal and feared commanders, linked to a string of bombings, beheadings and kidnappings, and the dispatching of suicide bombers.
He was killed three weeks ago fighting US-led troops in Helmand province.
A Taleban spokesman said on Thursday that Mullah Dadullah's family members had received his body in the old city of Kandahar and had reburied it in a city graveyard.
The government said later four Afghan hostages had been released by the Taleban.
A spokesman for the health ministry, Dr Abdullah Fahim, said the four men, who worked for the ministry, had arrived at the regional health directorate in Kandahar province.
He said there was no news of the fifth hostage, but that the four said they had been separated from him a few days ago.
Dadullah was a feared and brutal commander
Musa, one of the freed hostages, said he and his colleagues had been released in Gereshk district of Helmand province on Thursday morning, before officials took them to Kandahar.
"This morning the Taleban blindfolded us and put us in a vehicle," Musa told the Associated Press news agency.
"In Gereshk they opened our eyes and told us to go since our relatives were waiting."
The five male health workers - a doctor, three nurses and their driver - were abducted after administering vaccines in a refugee camp.
Their captors alleged that the government had failed to honour a pledge to release Dadullah's body.
Our correspondent says this was despite the interior ministry announcing the body was ready for collection and President Hamid Karzai repeatedly ordering that it be handed over.