Supporters of ousted president Mohamed Morsi cancelled some Cairo marches Sunday for "security reasons", as the country's military chief vowed to face down violent protests following Egypt's bloodiest week in decades.
The latest developments come as senior European Union diplomats were to hold emergency talks Tuesday in Brussels to discuss the situation in Egypt and future EU action.
More than 750 people were killed in four days of violence after the military and police launched a blistering crackdown on Islamist protest camps, sparking international condemnation.
In his first remarks since the campaign began on Wednesday, military chief Abdel Fattah al-Sisi said security forces would confront further violence from protesters.
"We will never be silent in the face of the destruction of the country," Sisi told top military and police commanders.
"We are very prepared for this," he said, pledging a "forceful" response to further attacks on police stations and government buildings.
The Islamists said they cancelled "several marches," citing fears of vigilantes and snipers but that others would go ahead.
"Several marches in Cairo have been cancelled for security reasons," said Yasmine Adel, a spokeswoman for the Anti-Coup Coalition of Morsi loyalists.
A separate statement by the group said "all nationwide marches and Cairo marches are continuing as planned" with the exception of a rally in the Roxy area of the capital.
At a mosque in the Dokki neighbourhood, where one march was scheduled to begin, residents stood guard.
"We are waiting for them. I swear we will kill them if they approach the mosque," one said.
In the evening the interior ministry issued a statement announcing a ban on vigilantes who have formed self-styled "popular committees" and urged citizens to respect a nightly curfew.
Earlier several hundred protesters briefly marched in the Suez canal city of Ismailiya, an AFP correspondent said.
Two policemen were later killed in a shooting attack near the city, the interior ministry said.
The rallies had been expected to be a test of the strength of Morsi's loyalists after four days of deadly clashes with police.
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On Saturday, police stormed a Cairo mosque where Islamists were holed up, after trading fire with gunmen inside its minaret.
On Sunday morning, the capital showed signs of returning to normal, with traffic beginning to flow again and banks and shops reopening for the first time since Wednesday.
Security forces on Wednesday stormed two camps of Morsi supporters, sparking clashes that killed at least 578 people across the country.
In the 24 hours after that, another 173 people were killed, according to the government, putting the four-day toll at 751.
The violence has shocked the international community, but Egypt's government -- installed by the army after Morsi's July 3 ouster -- has fiercely defended its actions.
The unrest, including a crackdown on Morsi's Muslim Brotherhood and the arrest of top Islamist leaders, has left Egypt divided as never before.
Vigilantes have pulled bearded men out of cars, and a mob chanted "terrorists" as Morsi supporters were dragged from Cairo's Al-Fath mosque on Saturday.
According to an AFP tally, more than 1,000 people have been killed since mass demonstrations against Morsi at the end of June, among them a son of the Brotherhood's supreme guide on Friday.
The government, meanwhile, dismissed reports that it could ban the Brotherhood.
Violence has also continued to plague the Sinai Peninsula, where a civilian, two soldiers and a policeman were killed overnight Saturday, security sources said.
The European Union said Sunday it would review ties with Egypt's army and government unless the bloodshed ends.
"The EU will urgently review in the coming days its relations with Egypt," EU leaders Herman Van Rompuy and Jose Manuel Barroso said.
British Foreign Secretary William Hague called his Egyptian counterpart Saturday to condemn violence by both sides, and described as "unacceptable" attacks against churches.
The United States has announced the cancellation of its biannual military exercise with Egypt, and its embassy in Cairo was closed Sunday for security reasons.
The White House has stopped short of suspending $1.3 billion in annual aid, although some US lawmakers called Sunday for the funds to be cut.
But the international response has not been uniformly critical. Both Saudi Arabia and Jordan have said they back Egypt in its fight against "terrorism."