The Egyptian interior ministry has urged protesters to leave camps in Cairo set up by supporters of deposed President Mohamed Morsi, one day after the army-backed interim government ordered it to take action against them.
In a statement read on state TV on Thursday, the interior ministry offered "a safe exit" to protesters who heeded the call.
No specified date has been decided upon for clearing out the sit-in, spokesman Hany Abdel Latif told Reuters news agency.
The ministry "calls on those in Rabaa al-Adawiya and Nahda squares to let reason and the national interest prevail, and to quickly leave," it said in a statement.
A day earlier, the interim government authorised police to break up the weeks-long protests, saying that officers will take "gradual steps" to disperse crowds.
Later on Thursday, Germany's Guido Westerwelle, the first foreign minister to visit Egypt since Morsi was deposed, urged authorities to avoid "the appearance of selective justice".
Speaking alongside his Egyptian counterpart Nabil Fahmy, he said: "There is no justice of vengeance and no selective justice. There is law and it applies to everyone."
Earlier, authorities said they had referred the leader of the Muslim Brotherhood, Mohammed Badie, and two other senior movement officials to a court on charges of inciting violence.
Following the warning against rallies, the US State Department urged Egypt to respect the right of peaceful assembly.
"We have continued to urge the interim government, officials and security forces, to respect the right of peaceful assembly," deputy spokeswoman Marie Harf told a news briefing. "That obviously includes sit-ins."
Morsi's supporters have been camped out in both squares demanding his reinstatement since July 3 when he was removed from power by the military.
The interior ministry later clarified Wednesday's statement, saying that police would take "gradual steps" to clear protesters.
Amnesty International said the decision to mandate security forces to end the pro-Morsi rallies is a "recipe for further bloodshed".
Follow our ongoing coverage of the political crisis in Egypt
"Given the Egyptian security forces' record of policing demonstrations with the routine use of excessive and unwarranted lethal force, this latest announcement gives a seal of approval to further abuse," said Hassiba Hadj Sahraoui, deputy director for the Middle East and North Africa at Amnesty.
"The authorities as well as the security forces should start with an approach that avoids the use of force and is based on ‘methods of persuasion, negotiation and mediation’, as recommended by international standards," she added.
More than 200 people have been killed in weeks of violence since the army deposed Morsi.
EU envoy Bernadino Leon was in Cairo on Wednesday to press the mediation effort.
US Republican senators John McCain and Lindsey Graham said on Wednesday that they would also visit Egypt to help quell violence and press for elections.
Speaking to Al Jazeera, Amr Abd Elaty, an expert on US-Egypt relations at the Al Ahram Research Centre, said: "There is a political division between the US Senate and White House, and right now there is a lot of pressure on President Barack Obama because some senators feel that he did not preserve relations with liberals in Egypt, he said.
"They think that he backed the Muslim Brotherhood, a group that many see as violent, oppressive and a threat to women’s rights."