GUNFIRE rings out and flames leap from burning cars on streets reeking of tear gas.

On bridges leading to and from Cairo's emblematic Tahrir Square, supporters and opponents of ousted Egyptian president Mohamed Mursi face off in bitter street battles. Egyptians are on edge this weekend, bracing themselves for yet more of the violence that has left at least 35 dead over the last few days across their increasingly divided country.

Enraged at his overthrow by millions of protesters backed by the country's powerful military, tens of thousands of Mursi's supporters are increasingly taking to the streets and holding rallies that they say will continue until the former leader is returned to office.

The clashes have accelerated after the supreme leader of Mursi's Muslim Brotherhood defiantly proclaimed his followers would not give up street action until the return of the country's first freely elected president.

"God make Mursi victorious and bring him back to the palace," Brotherhood chief Mohammed Badie proclaimed before cheering supporters at a Cairo mosque in his first appearance since the overthrow. "We are his soldiers. We defend him with our lives."

Yesterday, pro-Mursi protesters gathered in Cairo's Nasr City area, while the ousted Islamist president's opponents called for demonstrations today against the Muslim Brotherhood.

Alarmed by the rising violence in Egypt, both the United States and United Nations have expressed their concern.

The US state department urged Egypt's leaders to put a stop to the violence while UN Secretary-General Ban Ki-moon called for demonstrators to be protected.

"We call on all Egyptian leaders to condemn the use of force and to prevent further violence among their supporters," said state department spokeswoman Jen Psaki.

Ban's spokesman Farhan Haq said: "The Secretary-General believes strongly that this is a critical juncture in which it is imperative for Egyptians to work together to chart a peaceful return to civilian control, constitutional order, and democratic governance."

Yesterday, Egypt's new interim leader, Adli Mansour, held talks with the army chief and political leaders on how to pull the country out of the crisis.

The most populous Arab nation of 84 million people was thrown into its latest round of turmoil on Friday when tens of thousands of demonstrators across the country answered a call by Mursi's Muslim Brotherhood movement to stage a "Friday of Rejection".

The most deadly clashes were in the Mediterranean city of Alexandria, where 14 people died and 200 were wounded.

In central Cairo, rival protesters clashed late Friday into early yesterday morning with stones, knives, petrol bombs and clubs as armoured personnel carriers rumbled among them.

It took hours to restore calm on the Nile River bridges around the landmark Egyptian Museum. Anti-Mursi activists remained encamped in a suburb of the capital.

Mansour, installed to oversee a military roadmap to elections, spent his first day at the office at Ittihadiya Palace, where until a week ago Mursi ran Egypt.

Mansour held talks with the army chief and political leaders on how to pull the country out of the crisis.

He met armed forces chief General Abdel Fattah al-Sisi, who announced Mursi's ouster on Wednesday, and also held talks with former UN nuclear agency chief Mohamed ElBaradei, a leading liberal, and other politicians who had opposed Mursi.

ElBaradei, 71, is expected to be named the country's interim prime minister this weekend and lead a new administration focused on reviving a shattered economy and restoring civil peace and security.

In another development yesterday, a Coptic Christian priest was shot dead in Egypt's lawless North Sinai province in what could be the first sectarian attack since Mursi's overthrow, raising concerns about the potential for further religious violence.

Meanwhile, elsewhere in the Sinai peninsula adjoining Israel and the Gaza Strip, a new Islamist group announced its formation, calling the army's removal of Mursi a declaration of war on their faith and threatening violence to impose Islamic law.

Ansar al-Shariah (Supporters of Islamic Law) in Egypt said it would gather arms and start training members, in a statement on an online forum for Sinai militants recorded by SITE Monitoring.

The events of the last week have raised alarm among Egypt's allies in the West, including main aid donors the United States and the European Union, and in Israel, with which Egypt has had a US-backed peace treaty since 1979.

Back in Cairo yesterday, some 2000 people gathered outside the Republican Guard barracks where Mursi is being held. A man with a loudspeaker told soldiers separated from protesters by razor wire not to open fire.

Thousands more Islamists braved the fierce midday sun at a sit-in outside a nearby mosque. Shawled women shook their heads and wept as an imam led prayers for "martyrs" of the violence.

At least 15 tanks were positioned on streets leading to the square outside the mosque, but further away than on Friday, in a sign the military was keen to ease tensions.

Elsewhere in the capital, the retrial of former president Hosni Mubarak resumed at a snail's pace, in a bizarre coda to the past week's drama. The 85-year-old, who ruled Egypt for 30 years, is charged with conspiracy to murder hundreds of demonstrators in 2011.

The judge adjourned the case until August 17. He said he would continue to show proceedings live on state television, despite unhappiness among army commanders at seeing their former head of state and air force chief paraded in a courtroom cage.

In the days and weeks ahead Egypt will doubtless remain tense. According to analysts at the independent US based intelligence monitoring group Stratfor, any successor to Mursi will have to understand that his role will be to manage the affairs of the state while being a caretaker of the military's interests, and that it will be difficult to pursue a political agenda independent from the military's interests.

And all the while the military will be there, as it was on July 3 when it deemed it necessary to expel Mursi to maintain its grip on Egypt.

From Alexandria to Cairo, Egypt's streets look set to remain fiercely contested political battlefields for some time to come.