A spokesman for the interim president said Morsi's Muslim Brotherhood had been offered cabinet posts and would participate in the transition. The Brotherhood, Egypt's leading Islamist movement, dismissed the remarks as lies, saying it would never yield its demand for Morsi's return.
(Read More: Egypt announces criminal investigation of Morsi)
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.
Two people were killed at a bridge in central Cairo where police and local Morsi opponents clashed with some of his supporters who were blocking a route across the River Nile overnight. Another five were killed in the Cairo district of Giza, said the head of emergency services, Mohamed Sultan.
Mursi 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 killed 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 is mainly made up of technocrats and liberals, with an emphasis on resurrecting an economy wrecked by two and a half years of turmoil.
(Read More: Egypt Names Interim Prime Minister)
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 do not expect major reforms before a permanent government is put in place. The new planning minister, Ashraf al-Arabi, said on Monday that the Arab money would sustain Egypt through its transition and it did not need to restart talks with the International Monetary Fund on a stalled emergency 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. Arabi's comments could worry investors who want the IMF to prod reform.
Ahmed Elmoslmany, spokesman for interim President Adli Mansour, said the authorities expected the Brotherhood and other Islamists to agree to participate in national reconciliation and had offered them positions in the interim cabinet.
"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.
But senior Brotherhood figure Mohamed El-Beltagi said the movement had not been offered posts, and would reject 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.