There has been no independent confirmation of the claim.
But the United Nations responded to news of the execution-style killing with condemnation of the "senseless murder," and the UN called on authorities to bring those responsible to justice.
The case attracted particular attention when news emerged that the Afghan government had released militants in exchange for Italian hostage Daniele Mastrogiacomo, a journalist.
After his release in mid-March Mastrogiacomo reported having seen his captors behead his driver, Sayyed Agha, while conflicting reports of Naqshbandi's fate gradually gave way to word that he remained a hostage.
Afghans have rallied since Mastrogiacomo's release to protest suggestions that the central government had worked more actively for the Italian's release than for the freedom of its own citizens.
RFE/RL's Radio Free Afghanistan today quoted Shahabuddin Attal -- who claims to be spokesman for Taliban chief Commander Mullah Dadullah -- as saying that the Taliban executed Naqshbandi after the Afghan government did not meet their demands.
The head of Afghanistan's Independent Journalist Association, Rahimollah Samandar, suggested that such a killing could particularly affect independent media.
"We got news at 3:00 -- 3:00 p.m. today -- that Ajmal was killed by Taliban," Samandar said. "Two spokesmen for the Taliban [confirmed] that he was killed today at 3:00. So this is very bad news for Afghan journalists, especially for independent journalists. This is a very big loss in Afghan media, in Afghan journalism."
Mastrogiacomo, who was born in Pakistan and works for the Rome-based "La Repubblica," was reported kidnapped along with the two Afghans in early March and released about two weeks later.
Some 20,000 Italians demonstrated in Rome on March 31 for the release of Naqshbandi by the Taliban and another Afghan, Rahmatullah Hanefi, who reportedly was picked up by Afghan authorities following his intercession to help negotiate the release of Mastrogiacomo.
(with material from Reuters, AFP)