Soldiers and military police took down the makeshift tents of protesters who had camped out in Tahrir, or Liberation, Square, but scuffles broke out with some young men who refused to leave. Many local residents also shouted at the protesters that it was time to go.
The tension reflected the fragility of the situation as protesters press for a voice in guiding their country's move to democracy two days after Mr. Mubarak surrendered power to the military.
Egyptians continue their celebrations, a day after the 30-year rule of Hosni Mubarak came to an end. Video courtesy of Reuters.
The crowd on Tahrir Square was down from a peak of a quarter-million at the height of the demonstrations to a few thousand on Sunday. Most of those remaining have been pushed to sidewalks and the streets were open to traffic for the first time in more than two weeks. Thousands of volunteers descended on Tahrir Square on Saturday carrying brooms, dust pans and garbage bags and the streets surrounding it to clean up.
On Sunday, a coalition of youth and opposition groups that was the driving force of the movement pulled its supporters from the streets, calling instead for weekly mass demonstrations every Friday to keep pressure on. "It's time we show that we trust the army," said Nasser Abdel-Hamid, who is with the coalition.
The coalition is highly influential in the square, but its members don't claim to be leaders and often say they can't defy the will of the "revolution." Many in the square vowed to stay put until all their demands were met.
In its communiqué Saturday, the country's Supreme Council of the Armed Forces said the country "is committed to all regional and international obligations and treaties." Those treaties include its 1979 peace agreement with Israel.
Israeli Prime Minister Benjamin Netanyahu welcomed the announcement, saying the peace agreement "has greatly contributed to both countries and is the cornerstone of peace and stability in the entire Middle East."
The military rulers said Egypt's current cabinet would remain in power until a new government was formed. They pledged to insure "a peaceful transition of power in the framework of a free and democratic system." The new elected government "will rule the country to build a free democratic state," the statement said. It didn't set a timetable for the transition to democracy.
Egypt's Muslim Brotherhood said in a statement posted on its website Saturday that it wasn't seeking power or a majority of parliament seats. The group reiterated its previous assertion that it was only a participant in the Egyptian revolution and that its demands echoed those of the nation. It called on the army to rapidly form a new transitional government, scrap emergency laws, amend the constitution, ensure free elections and free all political detainees.
Mr. Mubarak stepped down Friday after 18 days of unrelenting protests, handing power to the military and opening the door to an uncertain new course for the Arab world's most populous country, and for the entire Middle East.
A number of senior government officials and former ministers were banned from traveling outside the country, including information minister Anas al-Fiqi and former prime minister Ahmad Nazif, state news media reported, citing court sources.
In a sign of attempts to restore normalcy, the military relaxed the hours of a nighttime curfew.
The country's stock market will reopen on Wednesday, the bourse said in a statement. It had planned to open on Sunday, after being closed since Jan. 27, two days after the start of the protests. In the last two days of trading before it closed, the exchange dropped 16%.
—Associated Press contributed to this article.