An influential Egyptian cleric has warned that using violence to break up sit-in protests by supporters of the ousted president Mohammed Morsi will lead to more bloodshed, hours after Egyptian authorities offered them "safe passage and protection" to end the demonstrations.

The offer by Egypt's Interior Ministry appears to be the first step in an effort by Egypt's new leadership to clear the more than a month-long protest by Morsi's followers in an eastern Cairo district and in the capital's twin city of Giza.

It came a day after Egypt's military-backed Cabinet ordered the ministry, which is in charge of the police, to clear the two sit-ins, arguing that they posed a threat to national security and terrorized citizens.

"The Interior Ministry ... calls on those in the squares of Rabaa el-Adawiya and Nahda to listen to the sound of reason, side with the national interest and quickly leave," Interior Ministry spokesman Hany Abdel-Latif said in a televised address.

"Whoever responds to this call will have a safe passage and protection," he added.

The offer also raised the specter of another bout of violence if security forces move in against the sit-ins in the eastern suburb of Nasser City and in Giza, outside the main campus of the Cairo University.

The Egyptian police have a track record of deadly crackdowns on street protests and Wednesday's Cabinet move in effect gave the police the ministry the mandate to act as they see fit.

Latif told Reuters Thursday that there is "no specified date" for the protesters to leave the sites.

In an emotional address aired by Al-Jazeera, the ultraconservative cleric Mohammed Haasan warned the military that a bloody confrontation would plunge it into conflict with the country's Islamists.

By Thursday afternoon, there were no significant actions against the protesters in either camp. An army helicopter flew low over the eastern Cairo sit-in, where protesters — many wearing helmets and carrying sticks — spoke of being ready for martyrdom. At one end of the camp, sandbags and bricks were erected against a possible attack.

Shortly before sunset, the demonstrators chanted "Execute el-Sissi!" and loudspeakers blared songs supporting Morsi.

"A revolution until victory — Morsi is back to the palace," one song went as men danced to the music.

The military ousted the Morsi in a July 3 coup after days of mass protests by millions of Egyptians demanding that he step down. Morsi's supporters have been staging marathon sit-in protests at two locations in Cairo.

He has been in detention since, along with several top leaders from the Muslim Brotherhood, the Islamist group from which he hails.

The Brotherhood insists that Morsi be reinstated and refuse to join the military-sponsored political process.

Senior Brotherhood leader Essam el-Erian was defiant in the face of the growing pressure, saying on his official Facebook page on Thursday that "the people will be victorious."

Brotherhood protester Saad Mohammed at the Giza sit-in sounded another defiant note, claiming that the number of protesters there grew after the government's warning.

"We are not afraid," he said.

At least 130 Brotherhood supporters have died in clashes with security forces since Morsi's ouster.

By early afternoon on Thursday there were no significant movements by Egyptian security forces against the protesters in either camp.

Earlier, the Interior Ministry had said it would not clamp down on the protesters but will take gradual measures including warnings, using water cannons and tear gas to minimize casualties.

The Associated Press contributed to this report.