By Ulf Laessing and Maggie Fick

CAIRO, July 17 (Reuters) - Egypt's interim government sets about the mammoth task of returning the country to civilian rule and rescuing the economy on Wednesday, a process complicated by deadly protests and a political stalemate with powerful Islamist groups.

Interim head of state Adli Mansour, the burly judge leading the army-backed administration, swore in 33 mainly liberal and technocratic ministers at the presidential palace on Tuesday.

He did not include a single minister representing either of Egypt's main Islamist groups that have won five straight elections since 2011.

Islamist President Mohamed Mursi was ousted by the military on July 3 after millions took to the streets to demand his resignation. Mursi's Muslim Brotherhood movement insists he be returned to power before it joins the political process.

The Brotherhood rejected the interim government led by Mansour and Prime Minister Hazem el-Beblawi, a veteran liberal economist.

"It's an illegitimate government, an illegitimate prime minister, an illegitimate cabinet," said Brotherhood spokesman Gehad El-Haddad. "We don't recognise anyone in it. We don't even recognise their authority as representatives of the government."

The ministers took up their posts hours after seven people were killed and more than 260 wounded when Brotherhood supporters clashed with police in central Cairo and nearby Giza.

The deaths took the number of people killed in clashes since Mursi's overthrow to at least 99.

The confrontations are increasingly polarising society between those who support the military intervention and those who oppose it.

As well as violence and political infighting, the interim government must also drag the Egyptian economy out of its torpor, after two and a half years of upheaval left state coffers and food stocks running dangerously low.

ECONOMY NEEDS FIXING

Saudi Arabia, the United Arab Emirates and Kuwait - rich Gulf Arab monarchies happy to see the fall of the Brotherhood - have promised a total of $12 billion in cash, loans and fuel.

But investors are sceptical that major reforms can be enacted before a permanent government is in place. Parliamentary elections are expected to be held in about six months.

New Planning Minister Ashraf al-Arabi has said Arab aid would sustain Egypt through its transition and that it did not need talks with the International Monetary Fund on a stalled loan.

Egypt sought $4.8 billion in IMF credit last year, but months of talks on the loan stalled with the government unable to agree on cuts in unaffordable subsidies for food and fuel.

In a development welcomed by investors, Mohamed Abu Shadi, formerly a senior interior ministry official responsible for investigating supply crimes, became supply minister.

Analysts said his appointment signalled a desire to clamp down on the theft of subsidised fuel, gas and bread and to reform an unwieldy state subsidy scheme that accounts for about a quarter of the budget.

"I see it as a signal of a very strong state," said John Sfakianakis, chief investment strategist at MASIC, a Saudi-based investment firm. "They want to stop leakages in the supply system."

ANGER RUNS DEEP

Thousands of Brotherhood supporters gathered early on Wednesday outside the Rabaa Adawiya mosque in northeastern Cairo, where they have endured stifling daytime heat and fasting to maintain a protest vigil that has lasted nearly three weeks.

Whenever the movement calls for marches, the evening crowd swells to tens of thousands as fierce resistance to Mursi's ouster shows little sign of abating in Cairo.

The seven deaths came after Brotherhood sympathisers clashed with riot police firing tear gas in the capital early on Tuesday. Two people were killed at a bridge across the Nile and five in the district of Giza.

It was the first such violence for a week and although more localised than protests that swept across Egypt on July 5, killing 35, scenes of angry mobs hurling rocks and petrol bombs at police in the capital has raised fears that the unrest could return any time.

In the worst single incident this month, troops shot dead 53 protesters at Cairo's Republican Guard compound. The military said it was a response to an attack, but the Brotherhood called it a "massacre". Four soldiers were also killed.

Mursi is being held incommunicado at an undisclosed location. Late on Tuesday, the public prosecutor ordered the start of official investigations into an old case accusing him and other Islamist leaders of planning a prison break during the 2011 uprising that ousted former President Hosni Mubarak.

In the lawless North Sinai province bordering Israel and the Gaza Strip, Islamist militants have called on Muslims to rise up against Egypt's military after Mursi's ouster.

At least 13 mainly security personnel have been killed there since July 3, and late on Tuesday assailants used rockets and machine guns to attack an Egyptian army camp near Rafah, a town straddling Sinai and Gaza. Two soldiers were wounded.

MILITARY TIGHTENS GRIP

One cabinet appointment in particular raised eyebrows.

Abdel Fattah al-Sisi, the general who deposed Mursi, was appointed Beblawi's first deputy while keeping his defence ministry portfolio, a move seen as consolidating the military's already dominant position in politics.

White House spokesman Jay Carney sidestepped questions about an appointment that is likely to further anger the Brotherhood.

"I don't have a specific response to ... any position that has been filled," Carney told reporters in Washington.

He said on Tuesday that Egypt, recipient of $1.5 billion in mostly military U.S. aid each year, was at a "critical stage."

"Egypt's future here is at stake," he said. "Certainly its potential for a democratic future is at stake."

Sisi said he overthrew Egypt's first freely elected president after only a year in power to enforce the will of the people, after millions protested against Mursi on June 30.

Brotherhood supporters have called the intervention a coup and see it as proof that Islamists will never be allowed to rule the Arab world's most populous country.

The United States has avoided calling Mursi's overthrow a "coup", because that would require it to halt aid.

Never comfortable with the rise of Mursi's Brotherhood, Washington nevertheless defended his legitimacy, a position that has attracted outrage from both sides in Egypt.

The crisis in a country straddling the strategic Suez Canal and which has a peace treaty with Israel has alarmed the international community.

The European Union's foreign policy chief Catherine Ashton arrives in Cairo on Wednesday in a fresh round of diplomacy to pressure rival parties to reconcile.

Egyptian politicians and Western diplomats said Mursi might still be in power had he grasped a political deal brokered by the EU with opposition parties in April. (Additional reporting by Mike Collett-White, Yasmine Saleh, Shadia Nasralla, Omar Fahmy and Peter Graff in Cairo and Lesley Wroughton in Washington; writing by Mike Collett-White; Editing by David Brunnstrom)