CAIRO (Reuters) - Tens of thousands of Egyptians packed into squares and marched along streets in Cairo on Friday to protest against the military overthrow of Islamist President Mohamed Mursi, and the United States called for the first time for him to be freed.
A large crowd of Mursi's Muslim Brotherhood supporters made its way along Ramses Street, close to Tahrir Square, and hundreds were on 6 October Bridge, where some of the worst clashes with anti-Mursi demonstrators took place a week ago.
On Tahrir, thousands more people gathered to attend a celebration of the holy fasting month of Ramadan, organised by groups who had called for Mursi's resignation.
The proximity of the rival factions, only a few hundred metres (yards) apart, raised concerns about more violence.
In last Friday's clashes between the toppled leader's supporters and opponents, 35 people were killed and hundreds wounded across the country.
Three days later, soldiers killed 53 Muslim Brotherhood supporters at the Republican Guard compound where Mursi is being held, in bloodshed that has deeply divided Egyptian society.
Four members of the security forces were also killed in that confrontation, which the military blames on "terrorists". Mursi's supporters call it a massacre and say those who died were praying peacefully when troops opened fire.
The Muslim Brotherhood's key demand is that he be reinstated, but for now, that looks like a lost cause.
Asked whether Washington agreed with the German Foreign Ministry's call for Mursi to be released, U.S. State Department spokeswoman Jen Psaki said: "We do agree."
She declined to say if the United States had officially conveyed its wish to Egyptian officials and the military.
At a Cairo mosque where Mursi supporters have held a vigil for more than two weeks, crowds swelled as people were bussed in from the provinces, where the Brotherhood has strongholds.
"We're here and we're not leaving," said Amer Ali, who drove the five-hour journey from the Nile city of Assiut with his wife and two young children to join tens of thousands of protesters.
"We came with our kids to support legitimacy, democracy, and our civilian president, the first freely elected president in the Arab world."
Many of Egypt's 84 million people have been shocked by the shootings, graphic images of which have appeared on state and private news channels and social media.
The Brotherhood contends it is the victim of a military crackdown, evoking memories of its suppression under Mubarak.
But many of its opponents blame Islamists for the violence, and some have little sympathy for the demonstrators who died, underlining how deep the fissures in Egyptian society are.
Islam Ibrahim, a Brotherhood member, was shot in the knee in Monday's violence, and still does not know if his brother Nasim, a soldier in the Republican Guard, was among those firing.
"I don't like to think about it. If he was (there), I know he wouldn't fire on unarmed demonstrators," he said.
The unrest has raised fear over security in the lawless Sinai peninsula bordering Israel and the Palestinian Gaza Strip.
Militant groups in North Sinai have promised more attacks and urged Islamists to take up arms, while the army has vowed to step up operations in the region, which is near the Suez Canal, the busy waterway linking Asia and Europe.
An Egyptian military helicopter briefly crossed into Israeli-controlled airspace over the Gaza Strip, in a possible sign of increased security jitters.
Security sources in Egypt and Israel both described the flyover as a navigational error, but it came shortly after militants killed an Egyptian policeman and wounded a second in an attack on a checkpoint in Sinai across the border from Gaza.
Egyptian military helicopters were also seen dropping flyers on a pro-Mursi rally in the town of Al Arish around 50 km (30 miles) from Israel's border, urging them to denounce violence.
Outside the Rabaa Adawiya mosque in northeastern Cairo, tens of thousands of Brotherhood supporters prayed and listened to speeches. Some of them have camped out in searing heat, fasting in the daytime since Ramadan began on Wednesday.
In a wooden shack erected on a side street and emblazoned with portraits of Mursi, men prepared vats of rice and lamb. Others put the food in plastic bags to distribute after sundown, when Muslims break their fast.
People squirted water from bottles to cool each other down. Others rested in the shade, dozing or reading the Koran.
The vigil began on June 28, as plans for the June 30 protests that drew millions of anti-government demonstrators to the streets gathered pace.
Since then, the camp has become the de facto base of the Brotherhood, whose leaders live under the threat of detention after prosecutors ordered their arrests earlier in the week.
Judicial sources say Mursi is likely to be charged, possibly for corruption or links to violence. Prosecutors are also looking again at an old case from 2011 when Mursi and other Brotherhood leaders escaped from prison after being detained during anti-Mubarak protests.
His son Osama told CNN that he was proud of Mursi.
"We back any decision you take. Even if you decided to leave the office. Your family, we are all proud of you, God bless you," he said in English.
The detentions and threats of arrest have drawn concern from the United States, which has walked a semantic tightrope to avoid calling Mursi's ousting a military coup.
U.S. law bars aid to countries where a democratic government is removed in a coup. Washington, which gives Egypt's military $1.3 billion in aid each year, has said it is too early to say whether Mursi's removal by the army meets that description.
The army has said it was enforcing the nation's will - meaning the huge crowds of people fed up with economic stagnation and suspicious of a Brotherhood power grab who took to the streets to demand Mursi's departure.
Crucial to longer-term stability will be holding parliamentary and presidential elections, which the transitional authorities are hoping to achieve in a matter of months.
Adli Mansour, the interim president named by the general who removed Mursi, has announced a temporary constitution, plans to amend it to satisfy parties' demands and a faster-than-expected schedule for parliamentary elections in about six months.
He has named liberal economist Hazem el-Beblawi as interim prime minister, and Beblawi said he had named centre-left lawyer Ziad Bahaa el-Din as his deputy. Beblawi also said he expected to swear in a cabinet next week.
Negotiations are difficult, with the authorities trying to attract support from groups that range from secularists to ultra-orthodox Muslims, nearly all of whom expressed deep dissatisfaction with elements of the interim constitution.
Rich Gulf states have thrown Egypt a $12 billion lifeline in financial aid, which should help it stave off economic collapse.
More than two years of turmoil have scared away tourists and investors, shrivelled hard currency reserves and threatened Cairo's ability to import food and fuel.
Additional reporting by Noah Browning, Mike Collett-White, Peter Graff, Ali Saed, Seham el-Oraby and Yasmine Saleh in Cairo, Nidal al-Mughrabi in Gaza, Ari Rabinovitch in Jerusalem and Arshad Mohammed in Washington; Writing by Mike Collett-White; Editing by Michael Roddy