Government spokesman Sofia Voultepsi said the vote would be held Dec. 17, with possible later rounds held in the following 12 days. The vote had not been expected to be held until late February.
The government needs the support from opposition lawmakers to avoid a stalemate and a snap general election, but is trailing in opinion polls to the anti-bailout Syriza party and facing widespread public discontent after a six-year recession.
The move was announced within an hour of Eurozone bailout lenders backing a Greek request to extend the rescue lending program for another two months.
Voultepsi said the presidential vote was shifted so Greece would be in a stronger position to negotiate with the lenders, who have provided €240 billion ($294 billion) in rescue funds in return for draconian spending cuts.
"The political uncertainty must end now," Voultepsi said.
Under voting rules, parliament requires a super-majority to elect a president, whose role is largely ceremonial, for a five-year term.
A presidential candidate must receive 200 votes in the 300-seat parliament to get elected, with a second round that would be held on Dec. 23 still requiring 200 votes, and a final third round on Dec. 29 needing 180.
Conservative Prime Minister Antonis Samaras' pro-bailout coalition has 155 lawmakers. It hasn't yet named a candidate to succeed 85-year-old Karolos Papoulias, whose second term expires in March.
"We are not surprised with this move. The government is running out of options, and wants to hide more austerity being demanded by (lenders) from the people," Syriza spokesman Panos Skourletis told the AP.
"They haven't got the 180 votes. And an earlier general election is welcome for us," Skourletis said. "Basically, the government just took a jump off the cliff."
AP Writer Demetris Nellas in Athens contributed.
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