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State newspapers on Monday published a sternly worded letter from Mr. Mubarak to his new prime minister, Ahmed Shafiq, ordering him to move swiftly to introduce political, legislative and constitutional reforms and pursue economic policies that will improve people’s lives.

But as news of the new government was heard in Tahrir Square, many of the protesters renewed chants of “We want the fall of this regime.”

Mostafa el-Naggar, a member of the Association for Change, said he recognized no decision Mr. Mubarak took after Jan. 25, the first day of Egyptian protests emboldened by Tunisians’ expulsion of their longtime president earlier in the month.

“This is a failed attempt,” said el-Naggar of the new government. “He is done with.”

If Egypt’s opposition groups are able to truly coalesce, it could sustain and amplify the momentum of the week-old protests.

But unity is far from certain among the array of movements involved in the protests, with sometimes conflicting agendas — including students, online activists, grassroots organizers, old-school opposition politicians and the fundamentalist Muslim Brotherhood, along with everyday citizens drawn by the exhilaration of marching against the government.

It was not clear how much the groups that met Monday represent everyone. The gathering of around 30 representatives, meeting in the Cairo district of Dokki, agreed to work as a united coalition and supported a call for a million people to turn out for a march Tuesday, said Abu’l-Ela Madi , the spokesman of one of the participating groups, al-Wasat, a moderate breakaway faction from the Muslim Brotherhood.

But they disagreed on other key points. The representatives decided to meet again Tuesday morning at the downtown Cairo headquarters of Wafd, the oldest legal opposition party, to finalize and announce a list of demands. They will also decide whether to make prominent reform advocate Mohamed ElBaradei spokesman for the protesters, Madi said.

Then, he said, they will march to Tahrir Square to demand the ouster of the 82-year-old Mr. Mubarak. The coalition also called for a general strike Monday, although much of Cairo remained shut down anyway, with government officers and private businesses closed.

The various protesters are united by little, however, except the demand that Mr. Mubarak go. Perhaps the most significant tensions among them is between young secular activists and the Muslim Brotherhood, which wants to form an Islamist state in the Arab world’s largest nation. The more secular are deeply suspicious the Brotherhood aims to co-opt what they contend is a spontaneous, popular movement.

Mr. ElBaradei, a pro-democracy advocate and former head of the U.N. nuclear watchdog, invigorated anti-Mubarak feeling with his return to Egypt last year, but the outlawed Muslim Brotherhood remains Egypt’s largest opposition movement.

In a nod to the suspicions, Brotherhood figures insist they are not seeking a leadership role.

“We don’t want to harm this revolution,” Mohamed Mahdi Akef, a former leader of the group.

Still, Brotherhood members appeared to be joining the protest in greater numbers and more openly. During the first few days of protests, the crowd in Tahrir Square was composed of mostly young men in jeans and T-shirts. Today, many of the volunteers handing out food and water to protesters are men in long traditional dress with the trademark Brotherhood appearance — a closely cropped haircut and bushy beards.

A wave of looting, armed robbery and arson that erupted Friday night and Saturday — after police disappeared from the streets — appeared to ease as police reappeared in many districts. Neighborhood watch groups armed with clubs and machetes kept the peace in many districts overnight.

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