Traffic is moving freely through Cairo's main square, which was ground zero of the revolution.
An eight-member panel entrusted to draw up constitutional amendments met for the first time on Tuesday. Those changes are expected within 10 days.
President Barack Obama praised Egypt's military council for working toward elections and a return of civilian control.
Meanwhile, Egypt's long-banned Muslim Brotherhood said it will form an actual political party once democracy is established. But the Brotherhood promised not to field a candidate for president, trying to allay fears at home and abroad that it seeks power.
The potential that the Brotherhood will emerge from Egypt's upheaval with greater influence has worried many Egyptians and others who fear a spread of Islamic militancy in the region. During his 29 years in power, former President Hosni Mubarak stoked such concerns at home and abroad, depicting his authoritarian grip as the only thing standing between Egypt and a Brotherhood takeover.
But many in Egypt contend the Brotherhood's strength is exaggerated.
Brotherhood, founded in the 1920s, has long been the most organized opposition movement. Though banned since 1954, the Brotherhood ran candidates for parliament as independents.
The group is eager to have a legitimate role after decades of suppression under Mubarak, whose regime arrested thousands of its members in regular crackdowns.
CBS News correspondent Lara Logan was recovering in a U.S. hospital Tuesday from a sexual attack and beating she suffered while reporting on the tumultuous events in Cairo.
Logan was in the city's Tahrir Square on Friday after Egyptian president Hosni Mubarak stepped down when she, her team and their security "were surrounded by a dangerous element amidst the celebration," CBS said in a statement Tuesday.
Separated from her crew in the crush of the violent pack, she suffered what CBS called "a brutal and sustained sexual assault and beating." She was saved by a group of women and an estimated 20 Egyptian soldiers, the network said. The Associated Press does not name victims of a sexual assault unless the victim agrees to it.
The attack on Logan, CBS News' chief foreign affairs correspondent, was one of at least 140 others suffered by reporters covering the unrest in Egypt since Jan. 30, according to the Committee to Protect Journalists. An Egyptian reporter died from gunshot wounds he received during the protests.
Logan joined CBS News in 2002. She regularly reports for the "CBS Evening News" as well as "60 Minutes," where she has been a correspondent since 2006. She has reported widely from Iraq and Afghanistan, and other global trouble spots.
The Associated Press contributed to this report.