In an ornate hall in the presidential palace, 33 cabinet ministers took turns being sworn in by Adli Mansour, a burly judge who was installed as interim president by the military when it toppled Islamist Mohamed Morsi on July 3.
The armed forces chief who removed Morsi, Abdel Fattah al-Sisi, was given the post of first deputy to interim prime minister Hazem el-Beblawi, a 76-year-old liberal economist tasked with implementing a "road map" to restore full civilian rule and repair a crumbling economy.
But Morsi's Muslim Brotherhood movement, which has said it would have nothing to do with politics until he was reinstated, dismissed the interim government as illegitimate.
"It's an illegitimate government, an illegitimate prime minister, an illegitimate cabinet. We don't recognise anyone in it. We don't even recognise their authority as representatives of the government," spokesman Gehad El-Haddad told Reuters.
The swearing-in ceremony was held after battles between Morsi's supporters and security forces that ran into the early hours of the morning, the worst violence in a week.
Two people were killed at a bridge across the Nile in central Cairo, and another five were killed in the district of Giza, said the head of emergency services, Mohamed Sultan. More than 260 people were wounded and more than 400 arrested.
Not one of the new ministers is from either Morsi's Brotherhood or Nour, the other main Islamist group, which together have won all five elections held in the two and a half years since autocrat Hosni Mubarak was toppled.
A spokesman for the interim president said the Islamists had been offered cabinet posts and would participate in the transition. The Brotherhood called the remarks lies, and said it would never yield its demand for Morsi's return.
Crisis in the Arab world's most populous state, which straddles the Suez Canal and has a strategic peace treaty with Israel, raises alarm for its allies in the region and the West.
Morsi's removal has bitterly divided Egypt, with thousands of his supporters maintaining a vigil in a Cairo square to demand his return, swelling to tens of thousands for mass demonstrations every few days.
Morsi is being held incommunicado at an undisclosed location. He has not been charged with any crime but the authorities say they are investigating him over complaints of inciting violence, spying and wrecking the economy.
A week of relative calm had suggested peace might be returning, but that was shattered by the street battles into the early hours of Tuesday morning, the bloodiest since more than 50 Morsi supporters were shot dead outside a barracks a week ago.
"We were crouched on the ground, we were praying. Suddenly there was shouting. We looked up and the police were on the bridge firing tear gas down on us," said pro-Morsi protester Adel Asman, 42, who was coughing, spitting and pouring Pepsi on his eyes to ease the effect of tear gas.
The new cabinet faces a dire task rebuilding an economy wrecked by two and a half years of turmoil.
Saudi Arabia, the United Arab Emirates and Kuwait - rich Gulf Arab states happy at the downfall of the Brotherhood - have promised a total of $12 billion in cash, loans and fuel.
Investors are sceptical that major reforms can be enacted before a permanent government is put in place. The new planning minister, Ashraf al-Arabi, said on Monday the Arab money would sustain Egypt through its transition and it did not need talks with the International Monetary Fund on a stalled loan.
Egypt had sought $4.8 billion in IMF aid last year, but months of talks ran aground with the government unable to agree on cuts in unaffordable subsidies for food and fuel.
Ahmed Elmoslmany, spokesman for the interim president, said the authorities expected the Brotherhood and other Islamists to agree to participate in national reconciliation.
"I am hoping and expecting, and I am in contact with members from the Muslim Brotherhood, and I can see there is an acceptance to the idea," he said.
Senior Brotherhood figure Mohamed El-Beltagi said the movement had not been offered cabinet posts, and would have rejected them if it had.
"We will not see reconciliation unless it's on the basis of ending the military coup," Beltagi said at a square near a Cairo mosque where thousands of Morsi supporters have maintained a vigil into its third week.
By sunrise calm had returned. The unrest has been less widespread than in the days after Morsi was toppled when 92 people died, but Egyptians still worry about continued violence.
At Tahrir Square, rallying point for anti-Morsi protesters, a Reuters reporter saw teenagers in civilian T-shirts being handed rifles by troops in an armoured vehicle.
It was not clear if they were civilians or security personnel in plain clothes.
Washington, which supports Egypt with $1.5 billion a year mainly for its military, has so far avoided saying whether it regards the military action as a "coup", language that would require it to halt aid.
The United States was never comfortable with the rise of Morsi's Brotherhood but had defended his legitimacy as Egypt's first elected leader. Its position has attracted outrage from both sides, which accuse it of meddling in Egypt's affairs.
The fast-paced army-backed "road map" to full civilian rule calls for a new constitution to be hammered out within weeks and put to a referendum, followed by parliamentary elections in about six months and a presidential vote soon after.
A former ambassador to the United States has been named foreign minister and a US-educated economist is finance minister. A police general was put in charge of the supply ministry, responsible for the huge distribution system for state-subsidised food and fuel.