Hazem al-Beblawi, who was appointed on Tuesday, said on Saturday that he would hold talks with the candidates for ministerial posts on Saturday and Sunday, in comments carried by the state-owned Akhbar al-Youm newspaper.
The new cabinet's top priorities will be to restore security, ensure the flow of goods and services and prepare for parliamentary and presidential elections, Beblawi said.
Beblawi is working according to a roadmap drafted by the military which overthrew Morsi on July 3 after millions took to the streets calling on him to step down.
Morsi, the country's first freely elected president, was accused of concentrating power in the hands of the Muslim Brotherhood, sending the economy into freefall and failing to protect minorities.
But his supporters argue that his removal from power was a flagrant violation of democratic principles and tens of thousands have taken to the streets to demand his reinstatement.
"There will be another mass protest on Monday," a Muslim Brotherhood spokesperson said on Saturday, a day after tens of thousands of Morsi's supporters rallied in Cairo.
Protesters are also expected to march on Monday to the Cairo headquarters of the elite Republican Guard, the scene of deadly clashes last week, the spokesperson, Tareq al-Morsi, said.
"It will be peaceful," he told Agence France-Presse.
Morsi to be released
On Friday, Washington and Berlin called on the military to release Morsi – who was detained just hours after the coup and is being held "in a safe place, for his safety", according to the interim leadership.
State department spokesperson Jen Psaki said the United States agreed with Germany's earlier appeal for Morsi to be released and was "publicly" making the same request.
Psaki said Washington wanted "an end to restrictions on Mr Morsi's whereabouts", while Germany suggested a trusted institution such as the International Committee of the Red Cross should be granted access to him.
On Friday, rival demonstrators rallied in the capital, but while there had been fears of fresh violence, the evening passed off peacefully.
Tens of thousands of Islamist protesters gathered outside the Rabaa al-Adawiya mosque in Cairo's Nasr City to pray and break their fast together on the first weekend of the holy month of Ramadan.
In Cairo's Tahrir Square and outside the Ittihadiya presidential palace hundreds of Morsi opponents sat down for their own iftar meals.
Morsi supporters have been camping outside the mosque, where many leaders of the Muslim Brotherhood have been holed up, some wanted by authorities.
"We will continue to resist," key Islamist leader Safwat Hegazi told Friday's crowd.
Democratically elected civilian government
"We will stay one or two months, or even one or two years. We won't leave here until our president, Mohamed Morsi, comes back," said the firebrand preacher, who is wanted by police for questioning on suspicion of incitement to violence.
Thousands also massed in support of Morsi outside the University of Cairo, watched over by a heavy security presence.
US President Barack Obama discussed the crisis in a phone call with King Abdullah of Saudi Arabia on Friday, a White House statement said.
Obama expressed "serious concern" about the violence since Morsi's overthrow and underscored the need to return to a democratically elected civilian government.
King Abdullah was the first foreign head of state to congratulate Egypt's interim president Adly Mansour, hours after he was named to replace Morsi.
Saudi Arabia and other Gulf Arab governments have also pledged $12-billion in assistance to shore up the faltering economy.
The interim authorities have been pressing ahead with forming a civilian administration but the Muslim Brotherhood has refused offers to join it.
Attacks by 'terrorists'
In the worst single incident of the recent violence, clashes outside the Republican Guard headquarters on Monday killed 53 people, mostly Morsi supporters.
The Brotherhood accuses the army of "massacring" its activists. The army says soldiers were attacked by "terrorists" and armed protesters.
Police are hunting Brotherhood chief Mohammed Badie and other senior leaders suspected of inciting violence, after arrest warrants were issued on Wednesday.
The military-appointed caretaker president has set a timetable for elections by early next year but Morsi opponents and supporters alike have criticised the interim charter he issued on Monday to replace the Islamist-drafted constitution. – AFP