br>By Maggie Fick and Peter Graff
CAIRO, July 10 (Reuters) - Egypt's prosecutor ordered the arrest on Wednesday of the leaders of ousted President Mohamed Morsi's Muslim Brotherhood, charging them with inciting violence that saw 55 of their members shot dead.
A week after the army toppled Egypt's first democratically elected leader, the bloodshed on Monday has opened fissures in the Arab world's most populous country, with levels of bitterness unseen in its modern history.
Brotherhood spokesman Gehad El-Haddad said the announcement of charges against leader Mohamed Badie and several other senior figures was a bid by authorities to break up a vigil by thousands of Morsi supporters demanding his reinstatement.
The leaders were charged with inciting the violence which began before dawn, when the Brotherhood says its followers were fired on while peacefully praying. The army says terrorists provoked the shooting by attacking its troops.
The past week's violence alarmed Western donors and Israel, which has a 1979 peace treaty with Egypt. Washington, treading a careful line, has neither welcomed Morsi's removal nor denounced it as a "coup", which under U.S. law would require it to halt aid including the $1.3 billion it gives the army each year.
The Brotherhood's downfall has been welcomed by wealthy Gulf states Saudi Arabia and the United Arab Emirates, which offered Egypt $8 billion in aid on Tuesday.
The charges against the Brotherhood leaders were "nothing more than an attempt by the police state to dismantle the Rabaa protest", Haddad said by telephone from the vigil at Rabaa Adaweya mosque in northeast Cairo. He said some of the leaders whose arrest was being sought were at the site of the protest.
"What can we do? In a police state when the police force are criminals, the judiciary are traitors, and the investigators are the fabricators, what can one do?"
In addition to Badie, prosecutors ordered the arrest of others including his deputy, Mahmoud Ezzat, and outspoken party leaders Essam El-Erian and Mohamed El-Beltagi.
The new interim prime minister on Wednesday reached for liberals to revive a shattered economy as he began forming a government to try to heal the bitterly divided nation. Egyptians had hoped the start of the Ramadan Muslim fasting month would cool passions but it has been overshadowed by rancour.
Hazem el-Beblawi, a 76-year-old economist and former finance minister named to head the cabinet on Tuesday, told Reuters he would start selecting ministers and would begin by meeting liberal politicians Mohamed ElBaradei and Ziad Bahaa el-Din.
Both are prominent figures in the National Salvation Front, the main secularist group that led protests against Morsi.
Both also support a stalled $4.8 billion loan deal with the International Monetary Fund, which would require Egypt to make politically painful reforms to subsidies for food and fuel that support its 84 million people but drain its finances.
Beblawi accepted that it would be a challenge to find a cabinet line-up with universal support. "I don't believe that anything can have unanimous approval," he told Reuters.
"Of course we respect the public opinion and we try to comply with the expectation of the people but there is always a time of choice. There is more than one alternative, you cannot satisfy all of the people."
BROTHERHOOD CONDEMNS "FASCIST COUP"
The Brotherhood has said it will have nothing whatsoever to do with a government of what it calls a "fascist coup".
Beblawi was named prime minister by the military-backed interim head of state installed after the army removed Morsi. ElBaradei, a former U.N. diplomat, has been named vice president. Bahaa el-Din, a former head of Egypt's investment authority, has been touted for senior posts.
The promised cash, loans and fuel from Saudi Arabia and the United Arab Emirates will go a long way to easing a deep economic crisis that has worsened during two and a half years of instability since autocrat Hosni Mubarak was swept from power by a popular revolt.
But the Gulf money could also reduce the incentive for Egypt to make the subsidy reforms the IMF says are needed to stabilise public finances, draw investment and rekindle economic growth.
Despite the violence that followed Morsi's removal, the interim authorities are proceeding with the army's "road map" to restore civilian rule. On Tuesday they announced a temporary constitution, plans to amend it, and a timetable for elections beginning in about six months.
Those moves already demonstrated the difficulty achieving political consensus, even among Morsi's opponents. The secularist NSF initially rejected the interim constitution, as did Islamists and others, although on Wednesday the NSF withdrew its rejection and issued a new, milder criticism.
Beblawi has indicated he would be open to offering cabinet posts to Islamists, including Brotherhood figures, although it seems impossible to imagine the Brotherhood accepting.
NOUR PARTY ASCENT
The authorities are courting the approval of Egypt's second largest Islamist group, the ultra-orthodox Nour Party, to demonstrate that Islamists will not be repressed as they were for decades under military-led rule.
Nour officially withdrew from politics in response to Monday's violence but has said it does not object to Beblawi's appointment and will assist his government.
Nour spokesman Nader Bakkar said on Wednesday the group would not accept posts in the new cabinet but would offer "consent and advice to help the cabinet pass through the transition period as soon as possible and with minimum damages".
"We are waiting to help. We are ready to advise but for the time being we still take the decision not to participate in the political process until the judiciary committee gives its report about what happened (on Monday)."
Bloodshed has abated since Monday's incident, the deadliest since Mubarak's fall, apart from a 2012 soccer stadium riot.
However, there are fears that the political violence could lead to a breakdown in security, especially in the lawless Sinai peninsula region bordering Israel.
Two people were killed and six wounded overnight when Islamist militants attacked a Sinai checkpoint.
On Tuesday Israeli troops found the remains of a rocket they believe was fired across the border from Egypt.