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The police, hated for their brutality and corruption under decades-old emergency laws, marched Sunday through Tahrir Square to the Interior Ministry, which oversees them. They demanded better pay and conditions but also sought to absolve themselves of responsibility for the police’s attempted crackdown that killed many demonstrators at the start of the protests.

“You have done this inhuman act,” one of the Tahrir protesters said to the police. “We no longer trust you.”

Hearing the accusations, Said Abdul-Rahim, a low-ranking officer, broke down in tears.

“I didn’t do it. I didn’t do it,” he implored. “All these orders were coming from senior leaders. This is not our fault. “

About 2,000 police demonstrated, at times scuffling with soldiers who tried to disperse them. Some troops fired gunshots in the air but later withdrew to avoid antagonizing the protesters. A few tanks remained outside the ministry.

“This is our ministry,” the police shouted. “The people and the police are one hand,” they chanted, borrowing an expression for unity.

Interior Minister Mahmoud Wagdy emerged from the building to talk to the police through a megaphone. He said they had a right to be angry.

“Give me a chance,” he said.

Separately, Egyptian troops scuffled with holdout protesters in Tahrir Square as the caretaker government sought to impose order, but outbreaks of labor unrest, including the police protest, underscored the challenges of steering Egypt toward stability and democratic rule.

There were also protests by workers at a ceramic factory, a textile factory and least two banks as Egyptians emboldened by the autocratic Mr. Mubarak’s fall sought to improve their lot in a country where poverty and other challenges will take years or decades to address.

Troops took down makeshift tents and made some headway in dispersing protesters who didn’t want to abandon their encampment in Tahrir Square, fearful that the generals entrusted with a transition to democratic rule will not fulfill all their pledges.

Still, most protesters had left the square in downtown Cairo, and traffic moved through the area for the first time. Many local residents shouted at the protesters that it was time to go.

The crowd on the square, the center of protests during the 18-day uprising, was down from a peak of a quarter-million at the height of the demonstrations to a few thousand on Sunday.

The Armed Forces Supreme Council is now the official ruler of Egypt after Mr. Mubarak handed it power. It consists of the commanders of each military branch, the chief of staff and Mr. Tantawi.

The military took power after pleas from protesters, and it has promised to ensure democratic change. The institution, however, was tightly bound to Mr. Mubarak’s ruling system, and it has substantial economic interests that it likely will seek to preserve.

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