Supporters of Egypt's ousted president Mohamed Morsi urged fresh rallies on Friday, raising fears of renewed violence as police prepared to disperse them amid international appeals for restraint.
The call came as US Secretary of State John Kerry said the military's removal in July of Morsi -- Egypt's first democratically elected president -- had been requested by millions.
In comments that will be seen in Egypt as supportive of the interim rulers, Kerry told Pakistan's Geo television: "The military was asked to intervene by millions and millions of people, all of whom were afraid of a descendance into chaos, into violence."
"And the military did not take over, to the best of our judgement -- so far. To run the country, there's a civilian government. In effect, they were restoring democracy," he added.
Allaa Mostafa, a spokeswoman for the pro-Morsi Anti Coup Alliance said that demonstrators would "continue our sit-ins and our peaceful protests" against what she termed a "coup d'Etat".
Morsi backers rejected an earlier offer from Egypt's interior ministry of a "safe exit" if they quickly left their Cairo protest camps, as police discussed how to carry out their orders from the military-installed interim government to end the protests.
In a statement, the ministry called on those in Rabaa al-Adawiya and Nahda squares "to let reason and the national interest prevail, and to quickly leave".
The ministry pledged "a safe exit and full protection to whomever responds to this appeal".
Authorities had already warned that the demonstrations would be dispersed "soon", but without saying when or how.
The stand-off raised fears of new violence, less than a week after 82 people were killed in clashes at a pro-Morsi rally in Cairo.
More than 250 people have been killed since the president's ouster following nationwide protests against his single year in power.
Meanwhile, diplomatic efforts to avoid further bloodshed gathered pace, with the European Union's Middle East envoy Bernardino Leon and German Foreign Minister Guido Westerwelle both arriving in Cairo to urge the rival camps to find common ground.
A senior member of the Freedom and Justice Party, the political arm of Morsi's Muslim Brotherhood, said the European envoys asked them to end their sit-ins.
"All the European delegates have the same message; they are pressuring the anti-coup protesters to disperse the sit-ins," said the official.
Following a meeting with Muslim Brotherhood representatives, Westerwelle warned that the situation was "very explosive".
"We have seriously and adamantly pressured for a peaceful solution. I hope that those concerned have gotten the message," he said in a statement.
"The international community has to keep up its diplomatic efforts, even though we don't know today whether these will prove successful."
Kerry also warned against further violence, saying the US was "very, very concerned" about the killing of dozens of pro-Morsi protesters in clashes with security forces and warning such loss of life was "absolutely unacceptable".
British counterpart William Hague also called for "an urgent end to the current bloodshed" and Morsi's release, in a phone call to interim vice president Mohamed ElBaradei, the Foreign Office in London said.
Amnesty International condemned the cabinet order as a "recipe for further bloodshed" but the mood was calm in Rabaa al-Adawiya square, where thousands of protesters have been camping out in a tent city, despite warnings from the authorities.
Foreign trade minister Munir Fakhry Abdel Nur said Wednesday's statement did not "give room for interpretation".
Accusing Morsi supporters of bearing arms, he said: "It is clear the interior ministry has been given the green light to take the necessary measures within legal bounds."
Egypt's interim government also faces an increase in militant attacks in the restive Sinai peninsula, where gunmen on Thursday shot dead a policeman in the northern town of El-Arish, security officials said.
Much of the Egyptian media expressed support for the government's decision, with some saying the interim administration had received "the people's mandate" in demonstrations last Friday backing Morsi's overthrow.
Further raising tensions on Wednesday, judicial sources said three top Brotherhood leaders, including Supreme Guide Mohamed Badie, would be referred to trial for incitement to murder.
Morsi himself has been formally remanded to custody on suspicion of offences when he broke out of prison during the 2011 revolt that toppled former president Hosni Mubarak.
He was detained hours after the coup and is being held at an undisclosed location, where EU foreign policy chief Catherine Ashton met him on Tuesday, later telling reporters he was "well".