By Shaimaa Fayed and Yasmine Saleh

CAIRO (Reuters) – President Hosni Mubarak, clinging to power despite unprecedented demands for an end to his 30-year rule, met on Sunday with the powerful military which is widely seen as holding the key to Egypt's future.

Mubarak held talks with Vice President Omar Suleiman, whose appointment on Saturday has possibly set the scene for a transition in power, Defense Minister Mohamed Hussein Tantawi, Chief of Staff Sami al-Anan and other senior commanders.

An earthquake of unrest is shaking Mubarak's authoritarian grip on power and the high command's support is vital as other pillars of his ruling apparatus crumble, analysts said.

Egyptians faced lawlessness on their streets on Sunday with security forces and ordinary people trying to stop looters after five days of popular protest.

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

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.

Amidst a heavy military presence, up to 4,000 people gathered 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.

"Hosni Mubarak, Omar Suleiman, both of you are agents of the Americans," shouted protesters, referring to the appointment of intelligence chief Suleiman as 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 many saw the appointment 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 shut. The bourse and the central bank said they 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.

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.

So far, the protest movement seems to have no clear leader or organization even if Mubarak did wish to open a dialogue.

Prominent activist Mohamed ElBaradei, a Nobel Peace Laureate for his work with the U.N. nuclear agency, returned to Egypt from Europe to join the protests. But many Egyptians feel he has not spent enough time in the country.

The Muslim Brotherhood, an Islamist opposition group, has also stayed in the background, although several of its senior officials have been rounded up. The government has accused it of planning to exploit the protests.

Thirty-four members of the Brotherhood, including seven of its leaders, walked out of prison on Sunday after relatives of prisoners overcame the guards, a Brotherhood official said.

The relatives stormed the prison in Wadi el-Natroun, 120 km (80 miles) northwest of Cairo, and set free several thousand of the inmates, Brotherhood office manager Mohamed Osama told Reuters. No one was hurt, he added.

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.

The tumult was effecting Egypt's tourist industry and the United States and Turkey said they were offering evacuation flights for citizens anxious to leave. Other governments advised their citizens to leave Egypt or to avoid traveling there.

Cairo airport was jammed with passengers eager to get out of the troubled country.

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, jewelry shops and government offices. Some suggested the chaos could herald a security forces crackdown.

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.

"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."

(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)