WRAPUP 4-Egyptians Face Lawlessness, Mubarak Hangs on

* Interior Ministry guarded by army armoured vehicles

* Heavy military presence replaces police

* Vigilantes protect Cairo buildings from mobs of looters

* Israel must exercise restraint, hopes for stability: PM

By Samia Nakhoul and Sherine El Madany

CAIRO, Jan 30 (Reuters) - Egyptians faced lawlessness on their streets on Sunday with security forces and ordinary people trying to stop looters after days of popular protest demanding an end to President Hosni Mubarak's authoritarian 30-year rule.

Throughout the night, Cairo residents armed with clubs, chains and knives formed vigilante groups to guard neighbourhoods from marauders after the unpopular police force withdrew following clashes with protesters that left more than 100 dead.

By morning, the capital's streets were mostly deserted, with the army guarding the Interior Ministry, and citizens putting their trust in the military, hoping they would restore order but not open fire to keep key U.S. ally Mubarak, 82, in power.

Up to 3,000 people gathered on Sunday in Tahrir Square, which has become a rallying point to express anger at poverty, repression and corruption in the Arab world's most populous nation. "The people want the fall of Mubarak," they chanted.

"Hosni Mubarak, Omar Suleiman, both of you are agents of the Americans," shouted protesters, referring to the appointment of intelligence chief Suleiman as a vice president, the first time Mubarak has appointed a deputy in 30 years of office.

It was the position Mubarak held before he become president and could set the scene for a transition of power. Many saw it as ending his son Gamal's long-predicted ambitions to take over.

"Mubarak, Mubarak, the plane awaits," demonstrators said.

Sunday is normally a working day in Egypt but banks and financial markets were ordered shut by the central bank. The bourse said it would stay closed on Monday.

The unprecedented turmoil has sent shock waves through the Middle East, where other autocratic rulers may face similar challenges, and unsettled financial markets around the globe.

Police beat and arrested students in central Khartoum, witnesses said on Sunday, as demonstrations inspired by events in Egypt broke out in the city demanding the government resign.

ARMY KEY TO EGYPT'S FUTURE

The protests bore many hallmarks of the unrest that toppled the leader of Tunisia two weeks ago, although the arrival of army troops to replace the police showed that Mubarak still has the support of the military, the country's most powerful force.

Army tanks and tracked vehicles stood at the capital's street corners, guarding banks as well as government offices and the Interior Ministry headquarters. State security fought with protesters trying to attack the building on Saturday night.

"We secured the Interior Ministry this morning and evacuated state security personnel. The ministry is empty," an army officer who did not want to be named told Reuters. "We're here for as long as it takes."

The tumult was effecting Egypt's tourist industry and the U.S. embassy said on Sunday it was offering evacuation flights to Europe for U.S. citizens who are anxious to leave the country.

Prime Minister Benjamin Netanyahu said on Sunday that Jerusalem must exercise responsibility and restraint in the face of the unrest and hoped that stability and peaceful ties would last with Egypt, the first Arab nation to make peace with Israel.

Egypt said it had shut down the operations of satellite broadcaster Al Jazeera which has shown footage of the demonstrations taking place in Cairo, Suez and Alexandria and heavy-handed police tactics to the rest of the Arab world.

The government has interfered with Internet access and mobile phone signals to try and disrupt demonstrators' plans. Twitter messages on Sunday were urging Egyptians to assemble at Tahrir Square to resume their anti-Mubarak message.

The United States and European powers were busy reworking their Middle East policies, which have supported Mubarak, turning a blind eye to police brutality and corruption in return for a bulwark against first communism and now militant Islam.

In Cairo, the biggest immediate fear was of looting as public order collapsed. Mobs stormed banks, supermarkets, jewellery shops and government offices. Some suggested the chaos could herald a security forces crackdown.

Thieves at the Egyptian Museum damaged two mummies from the time of the pharaohs.

On a main street in the Maadi district, groups of men stayed up through the night at barricades built from old lampposts, bits of wood and anything else they could find. A curfew went largely ignored.

In surreal scenes, soldiers from Mubarak's army stood by tanks covered in anti-Mubarak graffiti: "Down with Mubarak. Down with the despot. Down with the traitor. Pharaoh out of Egypt."

Asked how they could let protesters write anti-Mubarak slogans on their vehicles, one soldier said: "These are written by the people, it's the views of the people."

Residents expressed hope the troops would restore order. "People are terrified from these outlaws on the streets looting, attacking and destroying," said Salah Khalife, an employee at a sugar company.

SUCCESSION PLAN?

On Saturday, Mubarak bowed to protesters and appointed a vice-president for the first time, a move seen as lining up Suleiman as an eventual successor, at least for a transition period.

Egyptians say the changes mean nothing unless Mubarak goes.

"All these changes he made are sedatives," said Khalife. "People don't want Mubarak any more. People want change ... He doesn't want to leave. He is a thug."

In Washington, State Department spokesman P.J. Crowley said on Saturday: "The Egyptian government can't reshuffle the deck and then stand pat."

As in Tunisia, Egypt's exploding young population, most of them underemployed and frustrated by oppression at the hands of a corrupt and rapacious elite, were demanding a full clear-out of the old guard.

"This is the Arab world's Berlin moment," said Fawaz Gerges of the London School of Economics, comparing the events to the fall of the Berlin Wall in 1989. "The authoritarian wall has fallen, and that's regardless of whether Mubarak survives."

Saturday saw the worst bloodshed so far of the five-day uprising. Police shot dead 17 people in Bani Suef, south of Cairo. Various estimates put the overall death toll in the five days of unrest at more than 100. (Additional reporting by Dina Zayed, Marwa Awad, Shaimaa Fayed, Sherine El Madany, Yasmine Saleh, Alison Williams and Samia Nakhoul in Cairo, Alexander Dziadosz in Suez, Arshad Mohammed in Washington and Peter Apps, Angus MacSwan and William Maclean in London; Writing by Peter Millership, editing by Sonya Hepinstall)