Egypt is braced for further dramatic events on Friday as the vanquished Muslim Brotherhood called for a "day of rejection" following a widespread crackdown on its leadership by the country's new interim president, Adli Mansour.

Supporters of the ousted president Mohamed Morsi, still reeling from the military coup that removed their leader from power, are expected to take to the streets after Friday prayers following a series of raids and arrests that decimated the Muslim Brotherhood's senior ranks and consolidated the miltary's hold on the country.

In a stark sign of Egypt's new political reality, the group's supreme leader, Mohamed al-Badie, who was untouchable under Morsi's rule, was one of those arrested.

Gehad el-Haddad, a spokesman for the Muslim Brotherhood, said: "We are being headhunted all over the country. We are holding a mass rally after Friday prayers to take all peaceful steps necessary to bring down this coup." He called for demonstrations to be peaceful, despite fears that anger may spill over into violence.

State prosecutors announced on Thursday that Morsi, who is in military custody, would face an investigation starting next week into claims that he had "insulted the presidency" – a move that would appear to put an end to any hopes of a political resurrection.

At his inauguration on Thursday, Mansour, who was appointed as head of the constitutional court on Sunday, said this week's protests had "corrected the path of the glorious revolution that took place on 25 January 2011", and that continued revolution was needed until "we stop producing tyrants."

He also reached out to members of the Muslim Brotherhood, calling the organisation "part of the fabric of Egyptian society".

"They are just one of its parties and they are invited to integrate. If they answer the call, they will be welcomed," he told Channel 4 in his first interview.

Egypt's new interim president Adly Mansour has launched a widespread crackdown on the Muslim Brotherhood's leadership. Photograph: Khaled Desouki/AFP/Getty

But the severity of the crackdown on the Brotherhood leadership suggests that the overture will not be well received. Besides Badie, security officials also arrested his predecessor, Mahdi Akef, and one of his two deputies, Rashad Bayoumi, as well as Saad el-Katatni, head of the Brotherhood's Freedom and Justice Party, and the ultraconservative Salafi figure Hazem Abu Ismail, Associated Press reported.

Badie was arrested late on Wednesday from a villa where he had been staying in the Mediterranean coastal city of Marsa Matrouh and flown by helicopter to Cairo, security officials told AP.

The arrests of up to 300 Muslim Brotherhood officials are believed to have been ordered since the country's military commander, General Abdel Fatah al-Sisi, brought an end to Morsi's presidency on Wednesday night, a little over a year since he was inaugurated as the country's first democratically-elected leader.

The shockwaves have resounded in Egypt since then, with scenes of euphoria in the capital being met with foreboding in some towns and provinces, particularly in impoverished areas that had remained loyal to Morsi throughout the past turbulent year.

Hostility between the judiciary and Morsi's office had been a defining theme of his presidency. He had clashed heatedly with judicial leaders over the drafting of a new constitution, which was set aside yesterday.

Barack Obama said that he was troubled by Morsi's removal, and warned that US authorities were reviewing aid to Egyptian military – but he stopped short of calling the army's intervention a coup. He also condemned the arrest of Morsi and members of the Muslim Brotherhood.

The US president had invested political capital in establishing Morsi's democratic credentials, while maintaining ties to the Egyptian military, which had been the main beneficiary of $1.3bn (£850m) in US aid.

However, Egyptian military leaders also hold leverage over the US, primarily by maintaining a peace treaty with Israel as well as keeping the Suez Canal open and patrolling the strategically sensitive Sinai Peninsula.

Obama said: "We are deeply concerned by the decision of the Egyptian armed forces to remove President Morsi and suspend the Egyptian constitution. I now call on the Egyptian military to move quickly and responsibly to return full authority back to a democratically elected civilian government as soon as possible through an inclusive and transparent process, and to avoid any arbitrary arrests of President Morsi and his supporters."

One of the most senior Muslim Brotherhood members remaining at liberty also slammed the new military-backed order. "We declare our complete rejection of the military coup staged against the elected president and the will of the nation," said Abdel-Rahman el-Barr to the thousands gathered at a pro-Morsi demonstration in east Cairo. "We refuse to participate in any activities with the usurping authorities."

The place where it all began last Sunday, Tahrir Square, was quieter than at any time since on Sunday, with a sense of calm and normality returning to the area that had hours earlier been the scene of some of the biggest celebrations Egypt had ever witnessed.

Military jets flew a series of overflights in formation, an apparent display of triumph as much as support. A police helicopter also hovered over the square around the square for the first time since protests began, its pilot waving from the window at a cheering crowd below.

Elsewhere there were sporadic outbreaks of violence. In Zagazig, the Nile delta city where Morsi has a family home, 80 people were injured on Thursday, Reuters reported. Witnesses said the army moved in to seal the area after an attack on pro-Morsi protesters by men on motorcycles led to clashes with sticks, knives and bottles.

Multiple attacks by Islamist gunmen on security forces were reported in Sinai early on Friday, though it was unclear whether they were in reaction to Morsi's removal. Security sources said a soldier was killed and two were wounded when a police station in Rafah, on the border with Gaza, came under rocket fire.

Helicopters circled the Rabaa mosque in the east of Cairo, where Brotherhood supporters appear to be preparing for a long stay, despite the presence of military armoured columns not far away.

Men in hard hats, carrying improvised clubs and shields are guarding main entrances to the mosque area. "We are only here to defend ourselves," said Mohammed Ahmed, 35. "After what happened on Wednesday, anyone may come for us. Gangs, the police, the army. We will not let them win."