* Politicians disavow violence but still call for marches
* Nearly 60 people killed since Jan 25
* Opponents accuse Mursi of consolidating power
* Brotherhood says opposition trying to undo election outcome (Updates with petrol bombs thrown at presidential palace)
By Yasmine Saleh and Seham Eloraby
CAIRO/PORT SAID, Egypt, Feb 1 (Reuters) - Opponents of Islamist President Mohamed Mursi hurled petrol bombs at his palace on Friday as protesters returned to the streets of Egypt demanding his overthrow after the deadliest violence of his seven months in power.
Youths threw about two dozen petrol bombs and launched fireworks at the outer wall of the presidential compound in Cairo as night fell and thousands of peaceful demonstrators had dispersed.
Police fired water cannon and tear gas at the crowd. The roof of a building in the compound appeared to catch fire.
The head of the Republican Guard, which protects the palace, condemned the attack and what he described as attempts to climb the compound walls and storm one of its gates. In a statement to the state news agency, he urged the protesters to keep their demonstration peaceful.
Earlier there were scuffles in the central Tahrir Square, focal point of the revolution that overthrew authoritarian President Hosni Mubarak two years ago. Police fired tear gas at stone throwing youths. However there were no reports of serious bloodshed by nightfall.
Protests marking the second anniversary of the uprising that toppled Mubarak have killed nearly 60 people since Jan. 25, prompting the head of the army to warn this week that the state was on the verge of collapse.
Men dressed in mourning black marched through the Suez Canal city of Port Said, scene of the worst bloodshed of the past nine days, chanting and shaking their fists in one of the protests that brought thousands to the streets across the country.
"There is no God but God and Mohamed Mursi is the enemy of God," they chanted. Brandishing portraits of those killed in recent days, they shouted: "We will die like they did, to get justice!"
For the Port Said marchers, Friday was also the first anniversary of a soccer stadium riot that killed 70 people last year. Death sentences handed down on Saturday against 21 Port Said men over the riots helped fuel the past week's violence there, which saw dozens shot dead in clashes with police.
Mursi imposed a curfew and emergency rule in Port Said and two other canal cities on Sunday, a move that only seems to have added to the sense of local grievance.
Mohamed Ahmed, 26, protesting at the presidential palace, said: "I am here because I want my rights, the ones the revolution called for and which were never achieved."
Protesters also marched in other cities. In Alexandria they blocked major roads and staged a sit-in on the railway.
The protesters accuse Mursi of betraying the spirit of the revolution by concentrating too much power in his own hands and those of his Muslim Brotherhood. The Brotherhood accuses the opposition of trying to overthrow the first democratically elected leader in Egypt's 5,000-year history.
Friday's marches took place despite an intervention by Ahmed al-Tayyeb, head of the 1,000-year-old al-Azhar university and mosque, who hauled in politicians for crisis talks on Thursday where they signed a charter disavowing violence. Mursi's foes said the pact did not require them to call off demonstrations.
"We brought down the Mubarak regime with a peaceful revolution and are determined to realise the same goals in the same way, regardless of the sacrifices or the barbaric oppression," tweeted Mohamed ElBaradei, a former head of the U.N. nuclear watchdog who has become a secularist leader.
Leftist leader Hamdeen Sabahi said in a statement he would not enter talks until bloodshed was halted, a state of emergency lifted and those to blame for the violence brought to justice.
"Our aim ... is to complete the goals of the glorious January revolution: bread, freedom and social justice," he said.
Tahrir Square has become a graffitti-scarred monument to Egypt's perpetual turmoil, strewn with barbed wire and burnt out cars. Hundreds of protesters gathered in rain while vendors sold flag bracelets, pharaonic statues, sunflower seeds and water.
A man with a microphone shouted to a crowd of a few hundred, calling for Mursi to be put on trial.
"We came here to get rid of Mursi," said furniture dealer Mohammed al-Nourashi, 57. "He's only a president for the Brotherhood." As he spoke, a crowd gathered.
"Why is Obama supporting Mursi and the Brotherhood? Why?" a man shouted, challenging the U.S. president's policy on Egypt.
Osama Mohammed, 24, selling fruit from a battered wooden cart, said he graduated with a degree in commerce in 2007 but hadn't been able to find work - the sort of economic problems that caused the 2011 uprising and have only gotten worse since. He was not on the square for politics, just business.
"I've come every Friday because there's traffic," he said. "If the protests stay peaceful, it's no problem."
The rise of an elected Islamist after nearly 60 years of rule by secular military men in the most populous Arab state is the most important change achieved by two years of Arab revolts.
But seven months since taking power after a narrow election victory over an ex-officer, Mursi has failed to unite Egyptians and protests have made the country seem all but ungovernable. The turmoil has worsened an economic crisis, forcing Cairo to drain its currency reserves to prop up its pound.
Brotherhood leader Mohamed Badie, on his Facebook page, blamed the unrest on "regional and international forces which aim for instability and to stir up problems and ignite strife to damage Egypt ... to thwart the democratic transition".
Brotherhood followers have clashed with demonstrators in the past, especially at the presidential palace, but the group has kept its men off the streets during the latest violence.
It is far from clear that opposition politicians could call off the street demonstrations, even if they wanted to.
"You have groups who clearly just want a confrontation with the state - straightforward anarchy; you've got people who supported the original ideals of the revolution and feel those ideals have been betrayed," said a diplomat. "And then you have elements of the old regime who have it in their interests to foster insecurity and instability. It is an unhealthy alliance."
Many Egyptians are fed up.
"We are exhausted. This protests thing is a political game whose price the people are paying. I hate them all - liberals and Brotherhood," said Abdel Halim Adel, 60, near the presidential palace. (Additional reporting by Tom Perry and Alexander Dziadosz in Cairo, Abdul Rahman Youssef in Alexandria and Yusri Mohamed in Ismailia; Writing by Peter Graff; Editing by Paul Taylor)