Following on from the Taliban beheading the pair's Afghan driver, La Repubblica correspondent Mr Mastrogiacomo was released a fortnight ago after Kabul agreed to set free five Taliban resistance fighters in exchange.
However, the Afghan government's refusal to cooperate further with the hostage-takers in securing the release of one of their own citizens has sparked controversy at home and in Italy.
Mr Naqshbandi's death was announced by a Taliban spokesman today, but it has yet to be independently verified.
"We killed Ajmal today because the government did not respond to our demands," said Shohaabuddin Atal, Taliban commander Mullah Dadullah's official representative.
Speaking last week, Afghan president Hamid Karzai insisted that Mr Mastrogiacomo's case was an "extraordinary situation".
"[There will be] no more deals with no-one and with no other country," he added.
Taliban fighters are still holding at least ten hostages, including five government medics, two French humanitarian workers and three of their Afghan co-workers.
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