Egyptian cities were left strewn with rocks, glass and bullet casings on Saturday morning after almost 24 hours of violence which left 30 dead and more than 1,100 injured.

Clashes erupted on Friday night between supporters and opponents of ousted president Mohamed Morsi in central Cairo and other cities across Egypt , as fears of an expected backlash against his removal materialised.

Fighting broke out shortly after the Muslim Brotherhood's spiritual leader, Mohammed Badie – reported to have been arrested on Thursday – appeared unexpectedly at a rally in east Cairo on Friday evening to tell his followers to remain on the streets until Morsi's return. The ousted president had once been a senior member of the Islamist party.

In Cairo, a crowd of close to 5,000 Morsi supporters crossed the Nile over the 6 October Bridge, near the hub of opposition dissent, Tahrir Square. Turning left towards Maspero, the state television centre, they were approached by anti-Morsi demonstrators and fighting broke out in the streets.

Similar scenes were also reported in Egypt's second city, Alexandria, and there were reports of skirmishes in Luxor in the south of the country. The Sinai peninsula was placed on a state of emergency after an attack by gunmen on a local airport. There were also clashes reported in Damanhour, in Egypt's north-east, and Beni Suef, in the south, as Islamists protested across the country at Morsi's removal – in what the Brotherhood and other Islamist groups had billed as a "day of rejection".

Amid chaotic scenes near Tahrir, neither the army nor police intervened for two hours in what was the area's first glimpse of factional fighting since Morsi was forced from office on Wednesday. Live ammunition was heard as the two sides pelted each other with fireworks and stones. Molotovs were thrown and a car was burned out in clashes that ended only once the army sent several armoured vehicles to calm the situation at about 10pm.

Tensions were already high after security forces guarding Morsi shot and killed at least three of his supporters protesting outside the Republican Guards building in Cairo in which he was being held – and injured 15 more.

The shootings came as a Brotherhood official claimed that every single member of the organisation's leadership group had been arrested or was wanted by police, after new warrants were issued on Friday. A senior Brotherhood official claimed they were now being accused not just of insulting the judiciary, but of inciting murder.

Supporters and opponents of Egypt's ousted president Mohamed Morsi clash in Cairo on Friday evening. Photograph: Hassan Ammar/Associated Press

The violence against Morsi's supporters confirmed the worst fears of Islamists, who warned this week that they would face renewed violent oppression under the new military-backed regime.

Demonstrators at the scene said they had initially wanted to rescue the former president from captivity and escort him back to the presidential palace. But once the protesters – who marched on the Republican Guards building from two different mosques – arrived at about 3pm, they claimed that, in fact, they stayed back, chanting their support.

According to one eyewitness, the shootings began half an hour later, after a man left the crowd, approached a barbed-wire fence protecting the compound and fixed a Morsi poster to it. "Then he walked back," said Anas Abdel Rahim, a 19-year-old salesman with blood staining his hands after a teenager was shot in his arms. "Then someone wearing civilian clothes [on the army's side of the line] came to take the poster off the fence. People started shouting. He left it. He went to a soldier. They had a conversation. After the conversation the guy in civilian clothes started shooting."

Following the shots, protesters started running and security officials fired teargas and birdshot into the crowds – many of whom were caught unawares.

"They starting shooting, people started running, I was praying, and I got shot," said Ahmed Mohamed, bent over beside an ambulance as medics plucked birdshot pellets from his back.

The Guardian photographed live ammunition marked with army insignia at the scene. An army spokesman denied its involvement in the shooting.

Nearby a 50,000-strong pro-Morsi rally was held, where Brotherhood officials admitted that the immediate operational future of the party, a strictly hierarchical group that relies heavily on its leaders, was in disarray. With all the members of its top-level "Guidance Office" likely to be arrested soon, and most of its 200-strong, second-tier "Shura Council" seemingly also sought by police, the Brotherhood faces the most serious disruption to its operational capacity in decades. Senior Brotherhood officials appeared uncertain of who could take over in the event of Badie's arrest.

Asked who could succeed the organisation's spiritual leader, Mohamed Beltagy, a Brotherhood "guidance officer", replied: "Whoever remains in the Guidance Office." He said he expected to be arrested himself once he left the rally. After it was pointed out that no guidance officers might soon be left at liberty, Beltagy said: "These questions should be asked of the person that decided to leave the Brotherhood without leadership."

But Beltagy said the Brotherhood would survive. "Attempts to destroy [us] have been going on for 80 years and have never succeeded."

"We will go underground if we have to," said Salah Sultan, a senior official in the Brotherhood, and Egypt's deputy minister of Islamic affairs.

Egypt's new interim president, Adly Mansour, is expected to move into the country's presidential palace in north-east Cairo on Saturday – a compound occupied by Morsi aides only a few days ago. Mansour is expected to name the prime minister and may also name a cabinet, diplomatic sources said.

It was also announced that Egypt had been suspended from the African Union because of the circumstances of Morsi's departure.