Firing tear gas and rubber bullets, Egyptian riot police on Sunday clashed for a second day with thousands of rock-throwing protesters demanding that the ruling military quickly announce a date to hand over power to an elected government.

The police battled an estimated 5,000 protesters in and around central Cairo’s Tahrir square, birthplace of the 18-day uprising that toppled authoritarian leader Hosni Mubarak in February. Tear gas filled the air as protesters, many chanting “freedom, freedom,” pelted the police with rocks.

Sunday’s clashes, which come a day after two people were killed and hundreds wounded in similar violence in the capital and other cities, are stoking tensions eight days before the start of the country’s first post-Mubarak parliamentary elections. Public anger has risen over the slow pace of reforms and apparent attempts by Egypt’s ruling generals to retain power over a future civilian government.

“We have a single demand- The marshal must step down and be replaced by a civilian council,” said protester Ahmed Hani, referring Field Marshal Hussein Tantawi, Egypt’s military ruler and Mr. Mubarak’s longtime Defence Minister.

“The violence yesterday showed us that Mubarak is still in power,” said Mr. Hani, who was wounded in the forehead by a rubber bullet. He spoke over chants of “freedom, freedom” by hundreds of protesters around him.

Rocks, shattered glass and trash covered most of the ground in and around Tahrir early Sunday, while a cloud of white smoke caused by the use of dozens of tear gas shells hung in the air. Several hundred protesters were camping out on the lawn of the square’s traffic island, and protesters manning barricades into the square checked the IDs of anyone entering the plaza.

The windows of the main campus of the American University in Cairo, which overlooks the square, were shattered and stores were shuttered. “The marshal is Mubarak’s dog,” said one of a fresh crop of graffiti in the square.

Yahya el-Sawi, a 21-year-old university student, said he was enraged by the sight of riot police beating up protesters already hurt in an earlier attack by the security forces. “I did not support the sit-in at the beginning, but when I saw this brutality I had to come back to be with my brothers,” he said.

Many of the protesters had red eyes and coughed incessantly. Some wore surgical masks to fend off against the tear gas. A few fainted, overwhelmed by the gas.

Sunday’s clashes, which were mostly on a road leading from Tahrir to the Interior Ministry, appeared likely to grow.

Protesters were using social networking sites on the Internet to call on Egyptians to join them, and there were reports of several demonstrations headed to the square, including one from Cairo University.

The military, which took over from Mr. Mubarak, has repeatedly pledged to hand over power to an elected government but it has yet to set a specific date. According to one timetable floated by the military, the handover will take place after presidential elections are held late next year or early in 2013. The protesters say this is too late and accuse the military of dragging its feet. They want a handover to take place immediately after the end of parliamentary elections in March.

On Saturday, police fired rubber bullets, tear gas and beat protesters with batons, clearing the square at one point and pushing the fighting into surrounding side streets of downtown Cairo.

A 23-year-old protester died from a gunshot, said Health Ministry official Mohammed el-Sherbeni. At least 676 people were injured, he said. Another protester was killed in Alexandria, where clashes also took place, said a security official, speaking on condition of anonymity because he was not authorized to talk to journalists.

After nightfall, protesters swarmed back into Tahrir in the thousands, and running battles with the police in the streets took place throughout the night. Acrid smoke of tires set ablaze mixed with the stinging white smoke of tear gas.

The government urged protesters to clear the square.

A member of the military council, Maj. Gen. Mohsen el-Fangari, said protesters’ calls for change ahead of the election were a threat to the state.

“What is the point of being in Tahrir?” he asked, speaking by phone to a private TV channel. “What is the point of this strike, of the million marches? Aren’t there legal channels to pursue demands in a way that won’t impact Egypt ... internationally?”

“The aim of what is going on is to shake the backbone of the state, which is the armed forces.”

In a warning, he said, “If security is not applied, we will implement the rule of law. Anyone who does wrong will pay for it.”

Saturday’s confrontation was one of the few since the uprising to involve the police, which have largely stayed in the background while the military took charge of security. There was no military presence in and around the square on Saturday or on Sunday. The black-clad police were a hated symbol of Mr. Mubarak’s regime.

Some of the wounded had blood streaming down their faces and many had to be carried out of the square by fellow protesters to waiting ambulances. Human rights activists accused police of using excessive force.

Police arrested 18 people, state TV reported, describing the protesters as rioters.

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