CAIRO, Nov 23 (Reuters) - Protesters stormed the headquarters of the Muslim Brotherhood's party in Alexandria on Friday, throwing chairs and books into the street and setting them alight, after the Egyptian president granted himself sweeping new powers.

Supporters of President Mohamed Mursi and opponents also threw stones at each other near a mosque in the city, Egypt's second largest, a witness said.

Two cars had glass smashed as the clashes moved away from the area.

In Port Said, another port on the Mediterranean, hundreds of protesters gathered outside the Brotherhood's Freedom and Justice party headquarters and pelted it with rocks. Some tried to storm it but did not enter, another witness said.

In Cairo, thousands demonstrated against the decree issued on Wednesday night. (Writing by Edmund Blair; Editing by Angus MacSwan)