By Maggie Fick and Peter Graff

CAIRO, July 10 (Reuters) - Egypt's new interim prime minister reached for liberals on Wednesday to revive a shattered economy as he began forming a government to heal a nation bitterly divided by bloodshed a week after the elected president was overthrown.

Egyptians hoped the start of the Ramadan Muslim fasting month would cool passions that have raised animosity to a level unseen in the modern history of the most populous Arab state.

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 senior leaders of the National Salvation Front, the main secularist group that led protests against Islamist President Mohamed Mursi, toppled by the army last week after millions took to the streets against him.

Both are also outspoken supporters of a stalled $4.8 billion loan deal with the International Monetary Fund, which would require Egypt to make politically sensitive reforms to its ruinous subsidies of food and fuel.

Beblawi accepted that it would be a challenge to find a cabinet lineup with universal support: "I don't believe that anything can have unanimous approval," he said.

"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."

Beblawi was named prime minister by the military-backed interim head of state installed after the army removed Mursi. 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.

Thousands of Mursi supporters have been holding a vigil near a mosque in northeast Cairo for a week, demanding his reinstatement. At least 55 of them were killed on Monday in the worst violence in more than a year, when troops opened fire near a barracks where his supporters believe he is being held.

The Brotherhood says victims were peacefully praying; the army says terrorists provoked shooting by attacking its troops.

The violence has alarmed Western donors and Israel, which has a 1979 peace treaty with Egypt. Washington, treading a careful line, has neither welcomed Mursi'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.

However, 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 promised cash, loans and fuel 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 painful reforms the IMF says are essential to stabilise public finances, draw investment and rekindle economic growth.

ROAD MAP

Despite the violence that followed Mursi's removal, the interim authorities are proceeding briskly 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 Mursi'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 posts in his cabinet to Islamists, including Brotherhood figures, although it seems impossible to imagine the Brotherhood accepting such posts as long as it demands Mursi's restoration.

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.