* Rival demonstrators hurl stones, petrol bombs
* Washington urges dialogue to end crisis
* Mursi's vice president calls for consensus
By Edmund Blair and Marwa Awad
CAIRO, Dec 6 (Reuters) - Islamists battled with protesters outside Egyptian President Mohamed Mursi's palace on Thursday, after his vice president suggested amendments could be agreed to the draft constitution that has divided the nation.
Fires burned in the streets near the palace perimeter where opponents and supporters of Mursi threw stones and petrol bombs. Riot police tried to separate the two sides, but failed to halt fighting that extended from Wednesday into the early morning.
Residents, frustrated that police had not calmed the streets, set up makeshift road blocks nearby to check passers-by, scenes reminiscent of the popular uprising that toppled Mursi's autocratic predecessor Hosni Mubarak.
Five people were killed and 350 injured in the clashes, according to a statement released by the Ministry of Health.
"No to dictatorship," Mursi's opponents chanted, while their rivals chanted: "Defending Mursi is defending Islam."
Mursi's opponents accused him of creating a new autocracy by awarding himself extraordinary powers in a decree on Nov. 22 and were further angered when an Islamist-dominated assembly pushed through a draft constitution that opponents said did not properly represent the aspirations of the whole nation.
The United States, worried about the stability of a state that has a peace deal with Israel and to which it gives $1.3 billion in military aid each year, called for dialogue.
A presidential source said Mursi was expected to make a statement later on Thursday. His opponents had earlier called on him to address the nation to help calm the streets.
Bidding to end the worst crisis since Mursi took office less than six months ago, Vice President Mahmoud Mekky said amendments to disputed articles in the constitution could be agreed with the opposition. A written agreement could then go to parliament, to be elected after a referendum on the constitution on Dec. 15.
"There must be consensus," he told a news conference inside the presidential palace as fighting raged outside on Wednesday evening, saying opposition demands had to be respected.
Prime Minister Hisham Kandil called for calm to "give the opportunity" for efforts underway to start a national dialogue.
Protests spread to other cities, and offices of the Muslim Brotherhood's political party in Ismailia and Suez were torched.
But Mursi has shown no sign of buckling under pressure from protestors, confident that the Islamists, who have dominated both elections since Mubarak was overthrown in February 2011, can win the referendum and parliamentary election to follow.
On top of the support of the Brotherhood, which backed him for the presidency in the June election, Mursi may also be able to rely on a popular yearning for stability and economic revival after almost two years of political turmoil.
Egypt's opposition coalition blamed Mursi for the violence and said it was ready for dialogue if the Islamist leader scrapped the decree that gave him wide powers and shielded his decisions from judicial review.
"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," opposition coordinator Mohamed ElBaradei said on Wednesday.
"We are ready for dialogue if the constitutional decree is cancelled ... and the referendum on this constitution is postponed," he told a news conference.
But liberals, leftists, Christians, ex-Mubarak followers and others opposed to Mursi have yet to generate a mass movement or a grassroots base to challenge the Brotherhood.
Opposition leaders have previously urged Mursi to retract the 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 Mubarak from derailing a constitution vital for Egypt's political transition.
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.
British Foreign Secretary William Hague called for restraint on all sides. He said Egypt's authorities had to make progress on the transition in an "inclusive manner" and urged dialogue.
Both Islamists and their opponents have staged big shows of strength on the streets since Mursi's decree, each bringing out tens of thousands of people.
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.