Egypt's interim president has nominated Mohamed ElBaradei to serve as vice president and Ziad Bahaa el Din as prime minister, state television reported late Sunday.
Interim President Adly Mansour will need to get political consensus before they are appointed.
And presidential spokesman Ahmed Almoslemani stressed on state-run Nile TV there is no specific deadline of when the new government will be announced.
Nile TV had previously reported that he said an announcement would be made within 24 hours.
Earlier, ElBaradei's name had been floated for the office of prime minister, but a swearing-in announced for Saturday didn't happen.
Activist group Tamarod spokesman Mahmoud Badr told Egypt's OTV on Sunday that the presidency had tapped ElBaradei to form the new government but then retracted the offer after objections from the conservative al-Nour party.
ElBaradei is known around the world as the former head of the U.N. atomic watchdog agency, the International Atomic Energy Agency.
He was to appear Sunday in an interview with CNN's Fareed Zakaria but canceled it along with all other media interviews, his office said.
On the streets, the protests continue
The developments came as protesters took to the streets again, where, for weeks, arguments have turned to clashes.
Rocks have flown, knives have flashed and gunfire has cracked through the air, leaving bodies on the ground.
More than 30 people have died and 1,400 have suffered injuries since Wednesday's coup.
Supporters of the deposed president, Mohamed Morsy, and the Muslim Brotherhood rallied in Cairo to demand his reinstatement. Some of them took a vow Saturday before a cleric to die for their cause, if need be.
Protesters blocked a central street with barbed wire and stones, according to Nile TV.
On the other side of the city, opponents of Morsy packed Tahrir Square, shooting off celebratory fireworks.
They also gathered in the Nile Delta city of Damanhur, chanting and waving flags, the state-run Al-Ahram newspaper reported.
There were no reports of any clashes as darkness fell on Cairo. Still, some appeared to be bracing for violence.
Egypt's military said in a statement that it was stepping up security efforts for the demonstrations.
"We also warn against any provocation or clashes with the peaceful demonstrators," the statement said. "Anyone who violates these instructions will be dealt with firmly in accordance with the law."
Meanwhile, the Muslim Brotherhood's political party vowed that protests would be peaceful and accused authorities of planning to send fake bearded men into Cairo's Tahrir Square to incite violence.
"This is so they can claim that the supporters of the elected-president and the Islamic groups are attacking the peaceful demonstrators. ... We warn those who play with fire that any sectarian incitement at this critical time will not be in the interests of anyone in our beloved Egypt," the Freedom and Justice Party said in a statement posted on its Facebook page.
Human Rights Watch called for the country's military and political leaders to do more to stop the bloodshed.
"All sides need to tell their followers to refrain from actions likely to lead to violence and loss of life," Joe Stork, deputy Middle East and North Africa director at Human Rights Watch, said in a statement. "At the same time, the security forces need to show that they can act professionally and effectively to stop the violence without resorting to unlawful lethal force."
After Morsy was deposed, authorities arrested him and are holding him at an undisclosed location. His supporters believe he is being held at the Republican Guards complex and have targeted it with their marches.
On Friday, five of them died there, after security opened fire. On Saturday, members of the Muslim Brotherhood filed past the building with the coffins of those killed on their shoulders.