CAIRO, Nov 27 (Reuters) - Opponents of Egyptian President Mohamed Mursi will press ahead with a protest on Tuesday to demand the scrapping of a decree extending his powers, rejecting the Islamist's attempt to defuse a crisis that has brought violence back to Cairo's streets.

Mursi was accused of giving himself the powers of a modern-day pharaoh when he issued the decree last week that prevents legal challenges to any decision he takes until a new parliament is elected.

The president tried to ease tensions on Monday by agreeing to a compromise proposed by senior judges on the Supreme Judicial Council limiting the scope of presidential decisions that are immune from a court challenge.

But protesters camped out in Tahrir Square, the heart of the uprising that unseated Hosni Mubarak almost two years ago, said they would not leave until the decree was scrapped entirely.

"We came out in order to cancel the constitutional declaration completely," said Mohamed Fadel, 34, who was speaking among the tents that have been erected in the centre of Tahrir Square.

Violence has flared in the past when supporters and opponents of Mursi held rival protests. However, the Muslim Brotherhood, the group that propelled Mursi to office in this year's presidential poll, cancelled their own demonstration in Cairo also planned for Tuesday.

The crisis, the biggest since Mursi took office in June, has exposed deep divisions in the nation between Islamists and their opponents. It threatens to undermine Egypt's fragile economic recovery, signalled by an initial deal reached last week for a $4.8 billion loan from the International Monetary Fund.

Mona Amer, spokesman for the opposition movement Popular Current, said Tuesday's protest would go on. "We asked for the cancellation of the decree and that did not happen," she said.

Mursi's opponents have accused him of behaving like a dictator and the West has voiced its concern, worried by more turbulence in a country that has a peace treaty with Israel and lies at the heart of the Arab Spring.

One person has been killed and about 370 injured in violence since Mursi issued decree on Thursday, emboldened by international praise for brokering an end to eight days of violence between Israel and Hamas in Gaza.

UNREFORMED JUDICIARY

The decree was seen as targeting in part a legal establishment still largely unreformed from Mubarak's era. However, the Supreme Judicial Council, the nation's highest judicial body, proposed Mursi limit the scope of decisions that would be immune from judicial review to "sovereign matters", language the presidential spokesman said Mursi backed.

"The president said he had the utmost respect for the judicial authority and its members," spokesman Yasser Ali told reporters in announcing the agreement.

After reading out the statement outlining what was agreed with judges, Ali told Reuters: "The statement I read is an indication that the issue is resolved."

Mursi's administration has defended his decree as an effort to speed up reforms and complete a democratic transformation. Leftists, liberals, socialists and others say it has exposed the autocratic impulses of a man once jailed by Mubarak.

Before the president's announcement, leftist politician Hamdeen Sabahy said protests would continue until the decree was scrapped and said Tahrir would be a model of an "Egypt that will not accept a new dictator because it brought down the old one".

As well as shielding his decisions from judicial review, Mursi's decree protected an Islamist-dominated assembly drawing up a new constitution from legal challenge. Liberals and others say their voices are being ignored in that assembly, and many have walked out.

Only once a constitution is written can a new parliamentary election be held. Until then, legislative and executive power remains in Mursi's hands.

Though both Islamists and their opponents broadly agree that the judiciary needs reform, his rivals oppose Mursi's methods. (Additional reporting by Marwa Awad and Tom Perry; Writing by Edmund Blair and David Stamp; Editing by Jon Hemming)