“We’ll consider him free when he’s safely in Italian hands,” an Italian foreign ministry spokesman in Rome said.
Ettore Francesco Sequi, The ambassador in Kabul, also said he had no evidence of the release.
Taliban spokesman Yousuf Ahmadi told AFP that Mastrogiacomo and his Afghan translator were handed to elders in Helmand province after the government freed two members of the group, Latif Hakimi and Ustad Yasar.
But the Taliban also wanted another man, spokesman Mohammad Hanif, arrested in October, to be freed.
Ahmadi said: “Today, Hakimi and Yasar were released and we too handed over the journalist and his Afghan friend to the tribal elders. If Hanif is not released, we’ll take back the journalists.
“Once Hanif is released, the elders can take the Italian anywhere he wishes to go – we’ll let him go.”
The interior ministry and an intelligence agency spokesman said on Sunday they were not aware of any agreement to free any Taliban in custody.
The Italian embassy in Kabul also was unaware of any such agreement.
A provincial official confirmed the two Taliban were released late on Saturday night.
The pair were arrested in Pakistan in 2005 and later handed to Kabul.
Media reports said Mastrogiacomo’s driver was executed on Thursday.
The Taliban had threatened to execute the journalist unless its demands were met.
On Saturday, they extended their deadline to give Rome more time to respond.
Mastrogiacomo and his two colleagues were seized in the southern province of Helmand last week, where NATO and Afghan forces this month launched a major offensive, and the Taliban said he had confessed to spying for British troops.
La Repubblica denied he was a spy and said he had been working for it since 1980.