* Muslim Brotherhood calls another march
* Washington continues to walk diplomatic tightrope
* Concerns prompt U.S. Navy to move ships nearer
Supporters of ousted President Mohamed Mursi called for protests on Friday, and Egyptians prayed there would be no repeat of clashes that killed more than 90 people in the last week and left the Arab world's biggest nation bitterly divided.
Mursi's Muslim Brotherhood movement wants people to join it on the streets to push for Egypt's first freely elected leader to be reinstated, an aim that now seems in vain.
Officials say Mursi is still being held at the Republican Guard compound in Cairo, where troops killed 53 Islamist protesters on Monday in a clash that intensified anger his allies already felt at the military's decision to oust him.
Four soldiers were also killed in a battle the military says was started by terrorists. Mursi's supporters say those who died were praying peacefully when troops opened fire.
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 incident came just three days after 35 people were killed in clashes between pro- and anti-Mursi demonstrators across the country.
"It's a very hard time for Egyptians, to see footage of blood and violence during the holy month of Ramadan, and everyone I speak to says the same thing," said Fateh Ali, a 54-year-old civil servant in Cairo.
"I really hope the situation gets resolved soon. I don't think we can afford this economically or psychologically."
The Brotherhood believes it is the victim of a brutal military crackdown, evoking memories of when it was suppressed under longtime autocratic leader Hosni Mubarak. He was toppled in a popular uprising in 2011.
But many of its opponents blame Islamists for the violence, and some have little sympathy for demonstrators who died, underlining how deep the fissures in Egyptian society are.
VIGIL, SONGS FOR THE DEAD
Outside the Rabaa Adawiya mosque in northeastern Cairo, thousands of Brotherhood supporters gathered to mourn the dead in Monday's attack.
Women wailed and men cried as they watched a large screen showing graphic footage of hospital scenes immediately after the shooting, with corpses on the floor and medics struggling to cope with the number of bloodied casualties being carried in.
Hundreds of Egyptian flags fluttered in the evening breeze. Songs of defiance were sung.
Many thousands of Islamists have camped out in the area, braving searing heat and, since Wednesday, daytime fasting during Ramadan.
It has become the de facto base of the Brotherhood, whose leaders live under the threat of detention after the public prosecutor ordered their arrests earlier in the week.
Judicial sources say authorities are expected to charge Mursi in the coming days, although it is not clear for what.
The detentions and threats of arrest have drawn criticism from the United States, which has walked a diplomatic tightrope to avoid calling Mursi's ouster at the hands of the powerful Egyptian military a 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 the Egyptian events meet that description.
The Egyptian army said it was enforcing the nation's will after millions of people, fed up at economic stagnation and suspicious of a Brotherhood power grab, took to the streets at the end of June to demand his resignation.
State Department spokeswoman Jen Psaki said on Wednesday Mursi's government "wasn't a democratic rule."
Her words were warmly received by the interim government and swiftly denounced by the Brotherhood. But on Thursday, Psaki expressed concern over the crackdown on Brotherhood leaders.
"If politicised arrests and detentions continue, it is hard to see how Egypt will move beyond this crisis," she told a daily briefing on Thursday.
Underlining the level of concern overseas at Egypt's crisis, two U.S. Navy ships patrolling in the Middle East moved closer to Egypt's Red Sea coast in recent days, in what appeared to be a precautionary move following Mursi's ouster on July 3.
The United States often sends Navy vessels close to countries in turmoil in case it needs to protect or evacuate U.S. citizens or give humanitarian assistance. Their presence does not mean it is preparing for military action.
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 has scared away tourists and investors, shrivelled hard currency reserves and threatened its ability to import food and fuel.
Speaking to Reuters in a tent at a vigil by thousands of Mursi supporters, the ousted president's supply minister, Bassem Ouda, revealed that government stocks held just 500,000 tonnes of imported wheat, less than two months' supply.
Crucial to longer-term stability will be holding new 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 also has named liberal economist Hazem el-Beblawi as interim prime minister. Beblawi held his first meetings with political leaders on Wednesday and told Reuters that he expected the transitional Cabinet to be in place early 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.