* Rival factions hurl petrol bombs, stones outside palace
* Clinton calls for dialogue on contested constitution
* Vice president offers olive branch to opposition
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 off the ear of one of its members. Medical sources said 23 people had been wounded in clashes.
Riot police deployed between the two sides to try to stop the confrontations 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 had to be respected to reach a solution.
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.
Egypt's opposition coalition blamed Mursi for the violence around his palace and said it was ready for dialogue if the Islamist leader scrapped a decree he issued on Nov. 22 that gave him wide powers and shielded his decisions from judicial review.
"We hold President Mursi and his government completely responsible for the violence happening in Egypt today," opposition coordinator Mohamed ElBaradei told a news conference.
"We are ready for dialogue if the constitutional decree is cancelled ... and the referendum on this constitution is postponed," he said of the document written by an Islamist-led assembly that the opposition says ignores its concerns.
"Today what is happening in the Egyptian street, polarisation and division, is something that could and is actually drawing us to violence and could draw us to something worse," the former head of the U.N. nuclear watchdog added.
Opposition leaders have previously urged Mursi to retract the Nov. 22 decree, defer the referendum and agree to revise the constitution, but have not echoed calls from street protesters for his overthrow and the "downfall of the regime".
Mursi has said his decree was needed to prevent courts still full of judges appointed by ousted strongman Hosni Mubarak from derailing a constitution vital for Egypt's political transition.
Rival groups skirmished outside the presidential palace earlier 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."
Mekky said street mobilisation by both sides posed a "real danger" to Egypt. "If we do not put a stop to this phenomenon right away ... where are we headed? We must calm down."
U.S. Secretary of State Hillary Clinton weighed into Egypt's political debate, saying dialogue was urgently needed on the new constitution, which should "respect the rights of all citizens".
Clinton and Mursi worked together last month to broker a truce between Israel and Hamas Islamists in the Gaza Strip.
"It needs to be a two-way dialogue ... among Egyptians themselves about the constitutional process and the substance of the constitution," Clinton told a news conference in Brussels.
Washington is worried about rising Islamist power in Egypt, a staunch U.S. security partner under Mubarak, who preserved the U.S.-brokered peace treaty Cairo signed with Israel in 1979.
The Muslim Brotherhood had summoned supporters to an open-ended demonstration at the presidential palace, a day after about 10,000 opposition protesters had encircled it for what organisers dubbed a "last warning" to Mursi.
"The people want the downfall of the regime," they chanted, roaring the signature slogan of last year's anti-Mubarak revolt.
The "last warning" may turn out to be one of the last gasps for a disparate opposition that has little chance of scuttling next week's vote on the draft constitution.
State institutions, with the partial exception of the judiciary, have mostly fallen in behind Mursi.
The army, the muscle behind all previous Egyptian presidents in the republic's six-decade history, has gone back to barracks, having apparently lost its appetite to intervene in politics.
In a bold move, Mursi sacked Mohamed Hussein Tantawi, the Mubarak-era army commander and defence minister, in August and removed the sweeping powers that the military council, which took over after Mubarak fell, had grabbed two months earlier.
The liberals, leftists, Christians, ex-Mubarak followers and others opposed to Mursi have yet to generate a mass movement or a grassroots political base to challenge the Brotherhood.
Investors have seized on hopes that Egypt's turbulent transition, which has buffeted the economy for two years, may soon head for calmer waters, sending stocks 1.6 percent higher after a 3.5 percent rally on Tuesday.
Egypt has turned to the IMF for a $4.8 billion loan after the depletion of its foreign currency reserves. The government said on Wednesday the process was on track and its request would go to the IMF board as expected.
The board is due to review the facility on Dec. 19.
Elijah Zarwan, a fellow with the European Council on Foreign Relations, said that if Egypt was to find a compromise solution to its crisis, it would not be through slogans and blows.
"It will be through quiet negotiation, not through duelling press conferences, street brawls, or civil strife."