(Adds details and background)
BEIRUT, April 21 (Reuters) - Syria will hold a presidential election on June 3, the speaker of parliament said on Monday, setting a date for a vote likely to give President Bashar al-Assad a third term days after he said his forces were winning the country's civil war.
Assad is facing a three-year-old conflict against his rule that has killed more than 150,000 people and forced millions from their homes.
Under Syria's constitution the election is due by July, though the international powers that back Assad's opponents have described plans to hold it as a "parody of democracy".
Assad has not said whether he will stand in the election, but his allies in Russia and in Lebanon's Shi'ite movement Hezbollah have predicted he will stand and win.
Announcing the election on state television, parliamentary speaker Mohamed Jihad al-Laham said requests for nomination would be accepted until May 1. Voting for Syrians outside the country would take place at Syrian embassies on May 28, he said.
Assad said in mid-April that the conflict had reached a "turning point" due to his forces' military gains against the rebels, state media reported.
(Reporting by Alexander Dziadosz; Editing by John Stonestreet)