By Tom Perry

CAIRO, June 15 (Reuters) - Egyptian President Mohamed Mursi said he had cut all diplomatic ties with Damascus on Saturday and called for a no-fly zone over Syria, pitching the most populous Arab state firmly against President Bashar al-Assad.

Addressing a rally called by Sunni Muslim clerics in Cairo, the Sunni Islamist head of state said: "We decided today to entirely break off relations with Syria and with the current Syrian regime."

He also warned Assad's allies in the Iranian-backed Lebanese Shi'ite militia Hezbollah to pull back from fighting in Syria.

"We stand against Hezbollah in its aggression against the Syrian people," Mursi said. "Hezbollah must leave Syria - these are serious words. There is no space or place for Hezbollah in Syria."

Mursi, who faces growing discontent at home over the economy and over fears that he will pursue an Islamist social agenda, said he was organising an urgent summit of Arab and other Islamic states to discuss the situation in Syria, where the United States has in recent days decided to take steps to arm the rebels.

Mursi, who spoke at a packed 20,000-capacity stadium and waved Syrian and Egyptian flags after his entrance, also urged world powers not to hesitate to enforce a no-fly zone over Syria. The crowd of his supporters chanted: "From the free revolutionaries of Egypt: We will stamp on you, Bashar!"

Western diplomats said on Friday that Washington was considering a limited no-fly zone over parts of Syria. But the White House noted later that it would be far harder and costlier to set up one up there than it was in Libya, and said the United States had no national interest in pursuing that option.

Russia, an ally of Assad and fierce opponent of outside military intervention in Syria, said any attempt to impose a no-fly zone using F-16 fighter jets and Patriots based in Jordan would be illegal.

Egypt's U.S.-funded and -trained army is among the most powerful in the Middle East and effectively ran the country before the Arab Spring revolution of 2011 led to elections that saw Mursi, of the Muslim Brotherhood, take power a year ago.

There has been no suggestion, however, that Egyptian forces should get involved in the fighting in Syria.

Mursi said Syria was the target of "a campaign of extermination and planned ethnic cleansing fed by regional and international states", partly in reference to Iran, though he did not name the Shi'ite Islamic Republic.

Mursi said: "The Egyptian people supports the struggle of the Syrian people, materially and morally, and Egypt, its nation, leadership ... and army, will not abandon the Syrian people until it achieves its rights and dignity."

The Brotherhood has joined calls this week from Sunni Muslim religious organisations for a jihad against Assad and his Shi'ite allies. Egypt has not taken an active role in arming the Syrian rebels, but an aide to Mursi said this week that Cairo would not stand in the way of Egyptians who wanted to fight in Syria. (Additional reporting by Ali Abdellati; Writing by Alastair Macdonald; Editing by Kevin Liffey)