CAIRO (Reuters) - A leading Egyptian Islamic scholar brought together rival politicians on Thursday in a bid to ease a crisis that has triggered street violence killing more than 50 people, saying dialogue was the only way to resolve differences.

The meeting at Al-Azhar university and mosque, a respected seat of Sunni Islamic learning, brought together members of the Muslim Brotherhood - the Islamist group that propelled President Mohamed Mursi to power - with the president's most vocal opponents.

It was the first such meeting since the latest wave of violence erupted a week ago.

Reading from a document, Sheikh al-Tayyeb said national dialogue "in which all elements of Egyptian society participate, without any exclusion, is the only tool to resolve any problems or differences". Violence and bloodshed were forbidden, he said.

"Political work has nothing to do with violence or sabotage and the welfare of everyone, and the fate of our nation depends on respect for the rule of law," he said.

The participants included Mahmoud Ezzat, deputy leader of the Muslim Brotherhood, and Saad el-Katatni, the head of the Islamist group's political party.

Footage of the opening remarks broadcast by Al Jazeera showed them sitting across the table from liberal politician Mohamed ElBaradei, former head of the U.N. nuclear watchdog, leftist politician Hamdeen Sabahi, and former Foreign Minister Amr Moussa - prominent figures in an alliance of parties which is opposed to Mursi and has called for more protests on Friday.

Mursi has repeatedly urged his critics to join a national dialogue aimed at easing political tension in the country, but his opponents have spurned talks, demanding that he first meet demands such as forming a unity government.

The president side-stepped the issue on a visit to Germany on Wednesday, saying the next cabinet would be formed after parliamentary elections due in April.

(Writing by Tom Perry; Editing by Paul Taylor)