Opponents of Egypt's Mursi call Cairo protest for Tuesday

Egypt's President Mohamed Mursi speaks to supporters in front of the presidential palace in Cairo November 23, 2012.

CAIRO (Reuters) - Political parties angered by President Mohamed Mursi's decision to grant himself sweeping new powers have called on their supporters to protest against the move on Tuesday in Cairo.

Leftist, liberal, socialist parties and others have said their followers should march to Tahrir Square with the aim of "toppling the fascist, despotic constitutional declaration" issued by Mursi on Thursday, according to a statement from one of the parties.

"We are facing a historic moment in which we either complete our revolution or we abandon it to become prey for a group that has put its narrow party interests above the national interest," said the statement, issued by the liberal Dustour Party on its Facebook page late on Friday.

The marches will start at 5.00 p.m. (1500 GMT) from areas around the capital before converging on Tahrir Square, the epicentre of the uprising that swept Hosni Mubarak from power in 2011.

Mursi's decision to assume sweeping powers caused fury amongst his opponents and prompted violent clashes in central Cairo and other cities on Friday.

(Writing by Tom Perry; Editing by Andrew Osborn)