At least 36 people have died in more violence across Egypt as opposition grows to the expected appointment of the UN's former nuclear agency chief, Mohamed ElBaradei, as Prime Minister.
Mr ElBaradei was among liberal opponents of Mohammed Mursi who called for the huge protests against the Muslim Brotherhood.
Army-appointed interim head of state Adli Mansour held talks with the army chief and political leaders, including Mr ElBaradei, on the crisis.
He summoned Mr ElBaradei back to the presidential palace, state media reported, without giving more details.
His appointment is opposed by the Muslim Brotherhood but welcomed by some Western governments.
However Egypt's second-biggest Islamist group, the Nour Party, which has backed the military and its plan for a new political roadmap towards elections, has declared its opposition to Mr ElBaradei's installation.
Nour Party deputy leader Ahmed Khalil told the state news website Al-Ahram that the party would withdraw from the political transition process if Mr ElBaradei was confirmed in his post as expected.
"The nomination of ElBaradei violates the roadmap that the political and national powers had agreed on with General Abdel Fattah al-Sisi," he said, referring to the chief of the armed forces.
Meanwhile, a presidential spokesman said Egypt's Muslim Brotherhood movement can take part in new elections.
"We extend our hand to everyone, everyone is a part of this nation," the spokesman told reporters.
"The Muslim Brotherhood has plenty of opportunities to run for all elections including the coming presidential elections or the ones to follow."
A senior official in the Freedom and Justice Party, the Brotherhood's political wing, said the group rejected Mr ElBaradei's appointment as interim prime minister and described him as Washington's choice.
Overnight, fierce clashes in the Mediterranean city of Alexandria left 14 dead and 200 injured.
In Cairo, five people were killed as pro- and anti-Mursi protesters clashed in central areas and armoured personnel carriers rumbled among them to restore calm.
Five police officers were shot dead in separate incidents in the North Sinai town of El Arish.
A Coptic Christian priest was also shot dead in this afternoon.
He was attacked while walking in the Masaeed area of El Arish.
It was one of several attacks in the town believed to have been carried out by Islamists.
The Muslim Brotherhood has fiercely criticised Coptic Pope Tawadros, spiritual leader of Egypt's eight million Christians, for giving his blessing to the removal of the president.
Tens of thousands of people marched across the country yesterday in what the Brotherhood called a "Friday of Rage" to demonstrate against his overthrow and the army-backed interim government being set up to prepare for new elections.
Egypt's first freely elected president was toppled on Wednesday, the latest twist in a tumultuous two years since the fall of Hosni Mubarak in the Arab Spring uprisings that swept the region in 2011.
The events of the last week have aroused concern among Egypt's allies in the West, including key donors the United States and the European Union, and in neighbouring Israel, with which Egypt has had a US-backed peace treaty since 1979.
The fatalities added to the dozens of deaths in a month of unrest.
Last Sunday, huge rallies in Cairo and other cities called for Mr Mursi's resignation, venting anger over economic stagnation and perceptions of a Brotherhood power grab.
His overthrow was greeted with wild scenes of celebration but infuriated supporters who fear a return to the suppression of Islamists they endured under generations of military rule.