The most deadly clashes flared up in Port Said where 32 people were killed on Saturday alone. That violence was provoked by a court verdict sentencing 21 people, mostly from the city, to death for their role in a deadly stadium disaster last year.
But protests have been going in cities across Egypt since Thursday led by opponents of Mursi and his Islamist allies. Demonstrations were initially timed to mark Friday's second anniversary of the uprising that overthrew Hosni Mubarak.
Opponents say Mursi has betrayed the goals of the revolt.
The army, Egypt's interim rulers until Mursi's election June, were sent back onto the streets to restore order in Port Said and Suez, another port city on the Suez Canal where at least eight people have been killed in clashes with police.
Although scuffles continued on Sunday morning in Cairo, there was no immediate sign of the kind of deadly escalation of previous days in the capital or elsewhere.
The spasm of violence adds to the daunting task facing Mursi as he tries to fix a beleaguered economy and cool tempers before a parliamentary election expected in the next few months which is supposed to cement Egypt's transition to democracy.
It has also exposed a deep rift in the nation. Liberals and other opponents accuse Mursi of failing to deliver on economic promises and say he has not lived up to pledges to represent all Egyptians. His backers say the opposition is seeking to topple Egypt's first freely elected leader by undemocratic means.
"Till now, none of the revolution's goals have been realised," said Muhammad Sami, a protester in Tahrir Square. "Prices are going up. The blood of Egyptians is being spilt in the streets because of neglect and corruption and because the Muslim Brotherhood is ruling Egypt for their own interests."
On a bridge close to Tahrir Square, youths were hurling stones at police in riot gear who fired tear gas to push them back towards the square which was the cauldron of the uprising that erupted on Jan. 25, 2011 and toppled Mubarak 18 days later.
The US embassy in Cairo, which is near Tahrir Square, said it was suspending public services on Sunday "due to the security situation in the vicinity" of the mission.
Many Egyptians are frustrated by the regular escalations that have hurt the economy and their livelihoods.
"They are not revolutionaries protesting," said taxi driver Kamal Hassan, 30. "They are thugs destroying the country."Call for dialogue
The National Defense Council, headed by Mursi and including top army and other officials, has called for a national dialogue to discuss political differences.
That offer has been cautiously welcomed by the opposition National Salvation Front. But the organization has demanded a clear agenda and guarantees that any agreements will be implemented.
The Front, formed late last year when Mursi provoked protests and violence by expanding his powers and driving through an Islamist-tinged constitution, has threatened to boycott the parliamentary poll and to call for more protests if a list of demands is not met, including having an early presidential vote.
Egypt's transition has been blighted from the outset by political rows and street violence that have driven investors out and kept many tourists away, starving the economy of vital sources of hard currency.
Clashes in Port Said erupted after a judge sentenced 21 men to die for involvement in the deaths at a soccer match on Feb. 1, 2012 between Cairo's Al Ahly club and the local al-Masri team. Many of the victims were fans of the visiting team.
There were 73 defendants in the case. Those not sentenced on Saturday will face a verdict on March 9, the judge said.
Al Ahly fans cheered the verdict after threatening action if the death penalty was not meted out. But Port Said residents were furious that people from their city were held responsible, triggering wild rampages through the streets.
A security source in Port Said said 32 people were killed, many from gunshot wounds. More than 300 were injured in one of the most deadly eruptions of violence during the past two years.
Clashes have also flared in Cairo, Alexandria and Port Said. Eight people died in Suez on Friday and police clashed with protesters again on Saturday.
Officers fired teargas when protesters angry at Friday's deaths hurled petrol bombs and stormed a police post and other government buildings. Around 18 prisoners escaped from police stations and stole some weapons, a security source said.
Reflecting international concern, British Foreign Office Minister for the Middle East Alistair Burt said: "This cannot help the process of dialogue which we encourage as vital for Egypt today, and we must condemn the violence in the strongest terms."
European Union foreign policy chief Catherine Ashton urged the Egyptian authorities to restore calm and order and called on all sides to show restraint, her spokesperson said.
CAIRO (Reuters) -- Police fired tear gas at dozens of stone-throwing protesters in Cairo on Sunday in a fourth day of street violence that has killed at least 41 people and compounded the political challenges facing President Muhammad Mursi.