* Protests after Friday prayers could ignite new violence
* Army deploying at "vital installations" - state TV
* Muslim Brotherhood says not ready to retreat in battle (Adds army deployment report, revises death toll)
By Crispian Balmer and Yasmine Saleh
CAIRO, Aug 16 (Reuters) - The Egyptian military deployed around vital installations in Cairo, state media reported, before "Friday of Anger" protests called by backers of deposed President Mohamed Mursi.
Hundreds of people died and thousands were wounded on Wednesday when police cleared out two protest camps in Cairo set up to denounce the military's overthrow of Egypt's first freely elected president on July 3 and to demand his reinstatement.
The Health Ministry puts the death toll at 578. The Brotherhood says the government is hiding a much bigger number.
Dozens of armoured vehicles will close off streets around part of northeastern Cairo where Islamists had staged protests demanding Mursi's reinstatement, the state news agency said.
Military vehicles manned by soldiers could be seen in central Cairo, where checkpoints with barbed wire were set up.
Deeply polarised Egypt has been bracing for further confrontation expected after Friday prayers between members of Mursi's Muslim Brotherhood and the army-backed government.
The Brotherhood called for a nationwide march of millions to show anger at the ferocious security crackdown on Islamists.
After protesters torched a government building in Cairo on Thursday, the authorities said security forces would turn their guns on anyone who attacked the police or public institutions.
Wednesday's bloodshed was the third mass killing of Mursi's supporters since his ouster. The assault left his Muslim Brotherhood in disarray, but it said it would not retreat in its showdown with army commander General Abdel Fattah al-Sisi.
"After the blows and arrests and killings that we are facing, emotions are too high to be guided by anyone," said Brotherhood spokesman Gehad El-Haddad.
"PAIN AND SORROW"
A Brotherhood statement called for a nationwide "march of anger" by millions of supporters on Friday after noon prayers.
"Despite the pain and sorrow over the loss of our martyrs, the latest coup makers' crime has increased our determination to end them," it said.
The Brotherhood accuses the military of staging a coup when it ousted Mursi. Liberal and youth activists who backed the military saw the move as a positive response to public demands.
But some fear Egypt is turning back into the kind of police state that kept Mubarak in power for 30 years, as security institutions recover their confidence and reassert control.
Friday prayers have proved a fertile time for protests during more than two years of unrest across the Arab world.
In calling for a "Friday of anger," the Brotherhood used the same name as that given to the most violent day of the uprising against former President Hosni Mubarak. That day, Jan. 28, 2011, marked the protesters' victory over the police, who were forced to retreat while the army was asked to intervene.
In a counter-move, a loose liberal and leftist coalition, the National Salvation Front, called on Egyptians to protest on Friday against the Brotherhood's "obvious terrorism actions".
Signalling his displeasure at the worst bloodshed in Egypt for generations, U.S. President Barack Obama said on Thursday normal cooperation with Cairo could not continue and announced the cancellation of military exercises with Egypt next month.
"We deplore violence against civilians. We support universal rights essential to human dignity, including the right to peaceful protest," he said, but stopped short of cutting off the $1.55 billion a year of mostly military U.S. aid to Egypt.
The United States on Thursday told its citizens to leave Egypt due to the unrest. It issued the same advice last month.
The Egyptian presidency issued a statement saying Obama's remarks were not based on "facts" and would strengthen and encourage violent groups that were committing "terrorist acts".
"REFRAIN FROM VIOLENCE"
Washington's influence over Cairo has been called into question since Mursi's overthrow. Since then Saudi Arabia, Kuwait and the United Arab Emirates have pledged $12 billion in assistance, making them more prominent partners.
Obama's refusal so far to cut off U.S. aid to Egypt suggests he does not wish to alienate the generals despite the scale of the bloodshed in the army's suppression of Mursi supporters.
U.S. Defense Secretary Chuck Hagel said he had called Sisi on Thursday to say Washington would maintain its military relationship with Egypt, but he also told him the recent violence was putting defence cooperation at risk.
"Since the recent crisis began, the United States has made it clear that the Egyptian government must refrain from violence, respect freedom of assembly, and move toward an inclusive political transition," Hagel said in a statement.
The White House has voiced support for democracy in Egypt, while seeking to protect the U.S. strategic interest in Egypt's stability, its peace treaty with Israel and cooperation with the U.S. military, including privileged access to the Suez Canal.
France's foreign minister said on Friday the tension in Egypt risked playing into the hands of radical groups.
"Maximum restraint must be shown otherwise the risk is that extremist groups take advantage of the situation and that would be extremely serious, "Laurent Fabius told RTL radio.
The Egyptian press was full of praise for security forces, illustrating the rift between Cairo and its Western allies.
Some Gulf Arab states applauded the army action. The UAE praised Egypt's government for using "maximum self-control".
The Arab nations' cash, which started arriving in July, is aimed at stabilising Egypt's wobbling economy, which is suffering from a ballooning budget deficit and high inflation.
This week's carnage will further damage state coffers. The government has imposed a night-time curfew set to last at least a month, a move that will hit the crucial tourism industry.
On Thursday, the U.N. Security Council urged all parties in Egypt to exercise restraint, but did not assign blame.
"The view of council members is that it is important to end violence in Egypt," Argentine U.N. Ambassador Maria Cristina Perceval said after the 15-member council met on the situation.
Turkish Prime Minister Tayyip Erdogan had earlier also urged the council to convene quickly after what he called a massacre in Egypt and criticised Western nations for failing to stop it.
U.N. human rights chief Navi Pillay has called for an independent investigation into Wednesday's events in Egypt. (Additional reporting by Tom Perry, Michael Georgy, Alexander Dziadosz, Tom Finn, Ahmed Tolba and Omar Fahmy in Cairo, Steve Holland and Jeff Mason in Martha's Vineyard, Massachusetts, Andrea Shalal-esa in Washington and Stephanie Nebehay in Geneva; Editing by Alistair Lyon)