The Taliban later reportedly said they would extend the deadline after negotiations had taken place.
Massimo d'Alema, the Italian Foreign Minister later asked for more time to negotiate Mastrogiacomo's release.
"The complex affair... needs time," he said.
D'Alema denied that the Italian government was negotiating with the Taliban but said that contact had taken place via "humanitarian sources."
"Even the other side has perceived that an initiative is under way to find a solution," D'Alema said, without naming the Taliban.
"I want the other side to understand that the situation needs a reasonable time to develop and obtain the desired results."
Hanifi had said that the Italian and his Afghani translator would be released if the Kabul government agreed to release three Taliban prisoners.
Mastrogiacomo and his two colleagues were seized in the southern province of Helmand and the Taliban claimed that he had confessed to spying for British troops.
Mastrogiacomo appeared in a video released on Wednesday, appealing to the Italian government to work for his release.
US-led coalition forces have "mistakenly killed" five Afghan police officers during a clash in the southern Helmand province, according to the government.
There has been no immediate comment from the coalition's commanders.
The police were manning a checkpoint in the Gereshk district when the firefight broke out at around 7:00 pm (1430 GMT).
"Coalition forces mistakenly opened fire on police," said Zemeri Bashary, spokesman for the interior ministry. "Unfortunately five policemen were killed."
The incident comes as Nato-led forces are continuing their largest operation yet in Afghanistan, trying to secure a region of Helmand province which is a Taliban stronghold.
General Mohammad Esa Eftekhari, the provincial police chief of Helmand said the vehicle his men were travelling in may have been mistaken for one belonging to "enemy forces".
He said another six policemen went missing after the incident, and that they had most likely fled from the scene.
The general also said a team had been sent to the area to investigate the facts surrounding the shootings.
A spokeswoman for Nato said their troops were not involved in the incident.
Dozens of Afghan government soldiers have been been killed by foreign troops after being mistaken for Taliban militants.