By Yasmine Saleh and Marwa Awad

CAIRO, Dec 5 (Reuters) - Islamists fought protesters outside the Egyptian president's palace on Wednesday, while inside the building his deputy proposed a way to end a crisis over a draft constitution that has split the most populous Arab nation.

Stones and petrol bombs flew between opposition protesters and supporters of President Mohamed Mursi who had flocked to the palace in response to a call from the Muslim Brotherhood.

Two Islamists were hit in the legs by what their friends said were bullets fired during the clashes in streets around the compound in northern Cairo. One of them was bleeding heavily.

A leftist group said Islamists had cut the ear off one of its members, inflicting serious head wounds on him.

Riot police began to deploy between the two sides to try to end the violence which flared after dark despite an attempt by Vice President Mahmoud Mekky to calm the political crisis.

He said amendments to disputed articles in the draft constitution could be agreed with the opposition. A written agreement could then be submitted to the next parliament, to be elected after a referendum on the constitution on Dec. 15.

"There must be consensus," he told a news conference, saying opposition demands must be respected to overcome the crisis.

Opposition leader Amr Moussa, a former foreign minister and secretary-general of the Arab League, said Mursi should make a formal offer for dialogue if his opponents were to consider seriously Mekky's ideas for a way out of the political impasse.

"We are ready when there is something formal, something expressed in definite terms, we will not ignore it," Moussa told Reuters during talks with other opposition figures.

Opposition leaders have previously urged Mursi to retract a decree widening his powers, defer the plebiscite and agree to revise the constitution, but have not echoed calls from street protesters for his overthrow and the "downfall of the regime".


UNDER SIEGE

Mursi had returned to work at his compound a day after it came under siege from protesters furious at his assumption of extraordinary powers via an edict on Nov. 22.

The president, narrowly elected by popular vote in June, said he acted to stop courts still full of judges appointed by ousted strongman Hosni Mubarak from derailing a constitution meant to complete a political transition in Egypt, long an ally of Washington and signatory to a 1979 peace deal with Israel.

Rival groups skirmished earlier outside the presidential palace on Wednesday. Islamist supporters of Mursi tore down tents erected by leftist foes, who had begun a sit-in there.

"They hit us and destroyed our tents. Are you happy, Mursi? Aren't we Egyptians too?" asked protester Haitham Ahmed.

Mohamed Mohy, a pro-Mursi demonstrator who was filming the scene, said: "We are here to support our president and his decisions and save our country from traitors and agents."

Facing the gravest crisis of his six-month-old tenure, Mursi has shown no sign of buckling, confident that Islamists can win the referendum and a parliamentary election to follow.

Many Egyptians yearn for an end to political upheaval that has scared off investors and tourists, damaging the economy