Activists for and against ousted Egyptian president Mohamed Morsi have called rival rallies for the first Friday of Ramadan, as tensions soar over the army’s overthrow of the Islamist leader.

The Muslim Brotherhood, the influential group from which Morsi emerged, has vowed to keep protesting until he is reinstated, and has called separate rallies across Cairo.

But the group’s ability to mobilise remains in question with much of its leadership detained, on the run or keeping a low profile.

The anti-Morsi camp has also called for huge rallies after weekly Friday prayers, in Tahrir Square and at the Itihadiya presidential palace, with a mass iftar — the breaking of the Muslim fast — planned at sundown in the central plaza.

The rival rallies have raised fears of a fresh eruption of the violence that has shaken the country since the army removed Morsi from his post on July 3 after millions took to the streets demanding his resignation.

The overthrow of Egypt’s first democratically elected leader has sparked deadly clashes and deepened divisions as the Arab world’s most populous country marks the holy month of Ramadan, usually a time of communal sharing and unity.

In the worst violence since the political upheaval, clashes around an army building in Cairo on Monday left 53 people dead, mostly Morsi supporters.

The Brotherhood accuses the army of “massacring” its supporters, while the army says soldiers were attacked by “terrorists” and armed protesters.

The restive Sinai peninsula, home to Egypt’s luxury Red Sea resorts, has meanwhile been hit by a surge of violence, with militants killing an Egyptian police officer in a rocket attack on a checkpoint early on Friday, according to security and medical officials.

A Coptic Christian man was found decapitated on Thursday five days after gunmen kidnapped him, while on Wednesday, two people died in a militant attack on a security checkpoint in the Sinai and a police base came under mortar fire.

Hardcore Islamist militants have used the sparsely populated north of the peninsula as a launching pad for attacks on security forces.

The United States said it was pressing ahead with plans to deliver four F-16 fighters to Egypt, while urging the country’s interim leadership to halt arbitrary arrests of Muslim Brotherhood members.

Police are hunting for the movement’s Supreme Guide, Mohammed Badie, and other senior Brotherhood leaders, who are suspected of inciting deadly violence, after warrants were issued for their arrest on Wednesday.

The public prosecutor has pressed charges against 200 of 650 people detained during Monday’s violence.

A US state department spokeswoman said the arrests were “not in line with the national reconciliation” the interim government and military say they are pursuing, adding that if they continued “it is hard to see how Egypt will move beyond this crisis.”

There was no decision to halt the scheduled transfer of the warplanes or to cut off other security assistance to Egypt, a US official said on condition of anonymity, even though Washington has announced a review of all aid to Cairo.

Egypt’s ousted president is currently being held in a “safe place, for his safety” and has not yet been charged with anything, according to the foreign ministry, but military and judicial sources say he may eventually face charges.

Adly Mansour, the military-appointed caretaker president, has set a timetable for elections by early next year.

But opponents and supporters of Morsi alike have criticised the interim charter he issued on Monday to replace the Islamist-drafted constitution and steer a transition that the army itself has acknowledged will be “difficult”.

Many fear a repetition of the mistake of the last military-led transition, between Hosni Mubarak’s ouster in 2011 and Morsi’s election in June 2012.