Hazem al-Beblawi held talks with candidates for ministerial posts accompanied by vice president Mohamed ElBaradei and centre-left lawyer Ziad Bahaa Eldin, who is in the running for the post of deputy prime minister for economic affairs, the official MENA news agency reported. The consultations will continue on Sunday.
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, said Beblawi.
The premier 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.
The state prosecutor is investigating accusations filed by individuals that Morsi incited the killing of protesters and damaged the economy, judicial sources said.
Military and judicial sources have previously said he may eventually face charges.
Morsi's supporters say his removal from power was a flagrant violation of democratic principles and refuse to join an interim government as tens of thousands have taken to the streets to demand his reinstatement.
"There will be another mass protest on Monday," said Tareq al-Morsi, a Brotherhood spokesman said on Saturday, a day after tens of thousands of Morsi's supporters rallied in Cairo.
Protesters will also march on Monday to the Cairo headquarters of the elite Republican Guard, scene of deadly clashes last week, the spokesman told AFP, insisting it would be "peaceful."
Several thousand people attended a protest in central Tunis on Saturday, called by the country's ruling Islamist party Ennahda, against the military coup that deposed Morsi.
On Friday, Washington and Berlin called on the Egyptian military to release Morsi, who was detained just hours after the coup and is held in a secret location.
State Department spokeswoman 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 that the International Committee of the Red Cross should be granted access to him.
Rival demonstrators rallied in the capital on Friday, 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.
Morsi supporters have been camping outside the mosque, where many Brotherhood leaders have been holed up, some wanted by authorities.
Firebrand Islamist preacher Safwat Hegazi, who is wanted by police for questioning on suspicion of incitement to violence, said the crowds would pursue their protests for "one or two months or even one or two years."
In a phone call with Saudi King Abdullah on Friday, US President Barack Obama expressed "serious concern" about the violence since Morsi's overthrow and underscored the need to return to a democratically elected civilian government, the White House said.
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 pledged $12 billion in assistance to shore up the faltering economy.
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.