The independent Alsumaria broadcaster reported that Mahdi, who was also the commander of the Iraqi Armed Forces, ordered to remove the restriction beginning at 05:00 a.m., while an official TV channel specified that the curfew will be lifted beginning at 05:00 a.m. on Saturday.
However, the reports have not mentioned the area where the curfew will be lifted.
The measure was initially introduced in Baghdad early on Thursday but subsequently entailed several other Iraqi regions amid the unrest.
The Iraqi capital and southern regions have seen a wave of violent protests since Tuesday. Protesters demand the ouster of the government, as well as economic reforms and the end of corruption. The rallies have turned violent as law enforcement officers attempted to suppress the crowds. The security forces also reported about unidentified snipers shooting at both officers and demonstrators. The death toll in protests across the country has already reached 50, according to the Iraqi Observatory for Human Rights.
Baghdad maintains contacts with delegates of protesters from across Iraq to meet their demands, the office of Prime Minister Adel Abdul Mahdi said on Friday.
"We are currently in contact with an influential group of representatives of demonstrators in Baghdad. An agreement has been reached to meet their legitimate requirements," the office said.
The office also reported about "contacts with some representatives of demonstrators in Al Diwaniyah, Najaf and Dhi Qar, which resulted in the implementation of their legitimate demands."
Earlier, Mahdi said in a televised address that there was no "magic" solution to all problems, but promised payments to low-income families.