Ajmal Naqshbandi worked as a guide for visiting reporters
The group said it had killed Ajmal Naqshbandi because the government had refused to meet its demands to release senior figures from prison.
Italian reporter Daniele Mastrogiacomo was released after five Taleban members were freed in exchange. The driver, Sayed Agha, was beheaded last month.
Italian Prime Minister Romano Prodi has condemned Mr Naqshbandi's killing.
The two reporters and their driver were captured on 6 March in Helmand province.
Shohaabuddin Atal, a spokesman for Taleban commander Mullah Dadullah, said: "We killed Ajmal today because the government did not respond to our demands."
Italian deal
The Afghan government's intelligence services spokesman, Saeed Ansari, confirmed Mr Naqshbandi had been killed.
Mr Mastrogiacomo was freed in an exchange with Taleban prisoners
Tom Koenigs, UN special envoy to Afghanistan, said: "I condemn this senseless murder unreservedly and call on the authorities to bring those responsible to justice."
In Italy, Mr Prodi said he "learned with anguish" of Mr Naqshbandi's death. "We strongly condemn this absurd crime," he said.
Ajmal Naqshbandi worked as a guide and translator for visiting foreign reporters.
He was abducted with Mr Mastrogiacomo and their driver at a Taleban checkpoint and originally accused of spying for the British army.
The reporters' driver was beheaded to put pressure on negotiations for their release.
The BBC's Mark Dummett in Kabul says after intense lobbying from the Italians, a deal was done. Five Taleban were allowed to go and Mr Mastrogiacomo was set free.
Our correspondent says there was outrage in Afghanistan that the government would firstly bow to its enemy's demands and secondly that it would save a foreigner but not an Afghan.
The Taleban are still holding five government medics and two French aid workers along with three Afghan colleagues. Their fate will be decided next, they say.
President Hamid Karzai has ruled out any more hostage deals with the Taleban.
"[Mr Mastrogiacomo] was an extraordinary situation and won't be repeated again," Mr Karzai said on Friday. "No more deals with no-one and with no other country."
An Afghan interpreter, Ajmal Naqshbandi, kidnapped and held since March 5 by the Taliban in Afghanistan, was reported killed Sunday, according to a spokesman for the group.
Location of Helmand Province within Afghanistan
Naqshbandi was taken hostage in Helmand Province, along with Italian reporter Daniele Mastrogiacomo and their driver, Syed Agha. Mastrogiacomo was freed March 20 in a controversial hostage exchange, while Agha was killed by the Taliban early in his captivity.

The exchange of '''' reporter Mastrogiacomo for five Taliban prisoners was criticized, by security experts, as a precedent that could encourage further kidnappings. It was thought originally that Naqshbandi was also released as part of the exchange deal, but was later revealed by the Taliban that he was not released.

Mastrogiacomo and his editor at La Repubblica, Ezio Mauro, had made several appeals to the Afghan government to do what it could to secure the release of Naqshbandi. "This has already cost the life of Sayed Agha...we ask President Karzai to do all he considers just and possible to save Naqshbandi's life," said Mastrogiacomo and Mauro in their latest appeal.

The Taliban are holding two French aid workers and three Afghan colleagues, kidnapped last week in Nimroz Province, and are threatening to decide their fate next week. Ransom demands or deadlines have not yet been reported.

Afghan president Hamid Karzai, meanwhile, has ruled out any further exchange deals with the Taliban. 

A BBC correspondent in Afghanistan reported that there was outrage in Afghanistan over the exchange deal that saw the safe release of Mastrogiacomo. Afghans were incensed that the government not only gave in to Taliban demands, but would do so to save a foreigner and not an Afghan.