US Secretary of State John Kerry has said Egypt's military was "restoring democracy" when it ousted elected President Mohammed Morsi last month.
Mr Kerry said the removal was at the request of "millions and millions of people".
His remarks came as police prepare to disperse two pro-Morsi sit-ins in the capital, Cairo.
Egypt's interior ministry has promised Mr Morsi's supporters "safe exit" if they quickly leave the camps.
The country's cabinet on Wednesday ordered police to end the protests, calling them a "national security threat".
'Asked to intervene'
Washington has refused to describe Mr Morsi's removal as a "coup". Doing so would require the US government to cut off its estimated $1.5bn (£1bn) in annual aid to Egypt.
Correspondents say Mr Kerry's latest comments will be seen in Egypt as supportive of the interim government.
In an television interview in Pakistan, Mr Kerry said: "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."
Mr Kerry also warned against further bloodshed, according to AFP news agency.
He said Washington was "very, very concerned" about the killing of dozens of pro-Morsi protesters in clashes with security forces, calling it "absolutely unacceptable".
Thousands of supporters of Mr Morsi have defied new warnings from the military-backed cabinet by continuing their sit-ins.
The main protest camp is at a square near the Rabaa al-Adawiya mosque in the capital's north-east, where clashes left some 70 people dead last Saturday, and in Nahda Square near the main campus of Cairo University.
Demonstrators there have already ignored previous threats of dispersal.
They want to see Mr Morsi - Egypt's first democratically elected president - reinstated. The Islamist leader was removed by the army on 3 July, after just one year in office.
It came after mass rallies in which millions of Egyptians calling for his removal took to the streets.
Egypt's interior ministry released a statement on Thursday saying it called "on those in Rabaa al-Adawiya and Nahda squares to let reason and the national interest prevail, and to quickly leave".
The ministry "pledges a safe exit and full protection to whoever responds to this appeal", it added.
Ministry spokesman Hany Abdel Latif told Reuters there was "no specified date" for the removal.
Supporters of Mr Morsi and his Muslim Brotherhood movement have remained defiant.
Essam el-Erian, vice-president of the Freedom and Justice Party, the Brotherhood's political wing, said the protesters would not be deterred.
"There are expectations of a massacre taking place in front of the eyes of the whole world," he said.
"The free people in Egypt and the world must stand against this stupid cabinet mandate for the police to end the sit-in protests."
An African Union delegation confirmed on Wednesday that it had met Mr Morsi, who has not been seen in public since being ousted.
He had received no official visitors until Tuesday, when he met EU foreign policy chief Catherine Ashton who said he was "well".
The ousted leader has been formally remanded in custody at an undisclosed location, according to a judicial order.
He has been accused of the "premeditated murder of some prisoners, officers and soldiers" when he and several Muslim Brotherhood leaders were freed during a breakout at a Cairo prison in January 2011.
He is alleged to have plotted attacks on jails in the uprising that overthrew President Hosni Mubarak.
Mr Morsi is also accused of conspiring with the Palestinian militant group Hamas, which governs the Gaza Strip and has strong links with the Muslim Brotherhood.