* Protests flared during revolution anniversary
* Deadly Port Said riots erupted after court verdict
* Opponents say President Mursi betrayed revolution
* Islamists say critics undermine elected leader (Adds thousands attend Port Said funerals, shots heard)
By Edmund Blair
CAIRO, Jan 27 (Reuters) - Police fired teargas at dozens of stone-throwing protesters in Cairo on Sunday in a fourth day of street clashes that have killed at least 42 people and compounded the challenges facing President Mohamed Mursi.
In the worst violence, security sources said 33 people died in Port Said on Saturday when protests erupted after a court sentenced 21 people, mostly from the city, to death for their role in a deadly stadium disaster last year.
Thousands of mourners joined funeral processions for the dead in Port Said on Sunday, a witness said by telephone, adding that he heard gunshots and the sound of emergency vehicle sirens. But there were no immediate reports of new casualties.
Mursi's opponents have also taken to the streets across Egypt since Thursday, accusing him and his Islamist allies of betraying the uprising that overthrew Hosni Mubarak in 2011.
"None of the revolution's goals have been realised," said Mohamed Sami, a protester in Cairo's Tahrir Square on Sunday.
"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 hurled stones at police in riot gear who fired teargas to push them back towards the square, the cauldron of the uprising that erupted on Jan. 25, 2011 and toppled Mubarak 18 days later.
The latest protests were initially timed to mark Friday's anniversary of that revolt.
The U.S. and British embassies, both close to Tahrir, said they were closed for public business on Sunday.
The 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 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.
The army, Egypt's interim ruler until Mursi's election in June, was 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.
In Port Said, residents had reported gunshots overnight and shops and many workplaces were shut on Sunday. Residents said the city had been tense ahead of the funerals amid fears the burials could set off further violence.
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, referring to those gathered in Tahrir. "They are thugs destroying the country."
The National Defence Council, headed by Mursi, has called for a national dialogue to discuss political differences.
That offer has been cautiously welcomed by the opposition National Salvation Front. But the coalition 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 turbulence on the streets that have driven investors out and kept many tourists away, starving the economy of vital sources of hard currency.
Egypt's defence minister who also heads the army, Abdel Fattah al-Sissi, called for the nation to stand together and said the military would not prevent peaceful protests. But he called on demonstrators to protect public property.
Clashes in Port Said erupted after a judge sentenced 21 men to death for involvement in 74 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.
(Additional reporting by Shaimaa Fayed in Cairo and Yusri Mohamed in Ismailia; Editing by Janet Lawrence)