* 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 (Recasts, adds details from Port Said funeral)
By Edmund Blair and Shaimaa Fayed
CAIRO, Jan 27 (Reuters) - Gunshots rang out in Port Said on Sunday as people packed the streets for the funerals of 33 protesters killed at the weekend in the city, part of a wave of violence that has compounded challenges facing President Mohamed Mursi.
Some in the crowd chanted for revenge or shouted anti-Mursi slogans and teargas was fired in the vicinity, a witness said by telephone, adding that he heard emergency vehicle sirens after the shots were fired.
"Our soul and blood, we sacrifice to Port Said," people chanted, as the coffins were carried through the streets.
There were no immediate reports of further casualties in the city, where 33 people were killed on Saturday when residents went on the rampage after a court sentenced 21 people, mostly from the city, to death for their role in a deadly stadium disaster in Port Said last year.
Elsewhere in Egypt, police fired teargas at dozens of stone-throwing protesters in Cairo in a fourth day of clashes. Protests in the capital and other cities erupted at the end of last week over what the demonstrators say is a power grab by Islamists two years after Hosni Mubarak was overthrown.
The protesters accuse Mursi, elected in June with the support of his Muslim Brotherhood group, of betraying the democratic goals of the revolution. Since protesters hit the streets on Thursday, 42 people have been killed, most in Port Said and Suez, both cities where the army has now been deployed.
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.
"BLOOD BEING SPILT"
"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 U.S. and British embassies, both close to Tahrir, said they were closed for public business on Sunday.
The army, Egypt's interim ruler until Mursi's election, was sent back onto the streets to restore order in Port Said and Suez, which both lie on the Suez canal. In Suez, at least eight people were killed in clashes with police.
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.
Many ordinary 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."
CALL FOR DIALOGUE
The National Defence Council, headed by Mursi, called on Saturday for 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 pound has been hit hard by the turmoil, steadily weakening against the dollar despite efforts by the central bank to slow the fall and preserve foreign reserves now at critical levels. The latest violence has added to investors' concerns.
The Port Said clashes 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 Yusri Mohamed in Ismailia; editing by Philippa Fletcher)