-- After throngs of Egyptians put their lives on hold for more than two weeks, Egypt woke up Sunday to its first regular work day without longtime ruler Hosni Mubarak as president.

For the first time since demonstrators took control of Cairo's Tahrir Square -- the epicenter of mass protests that brought down Mubarak's nearly 30-year regime -- traffic was flowing freely through the area Sunday morning. Sunday marks the traditional start of the work week in Egypt.

"It's time to start rebuilding the country," activist Yehya Kheireldin said Saturday, pointing to the hundreds of volunteers with brooms who were sweeping away the debris from protests that lasted 18 days.

Wael Ghonim, the Egyptian activist whose Facebook page is credited with triggering the uprising, wrote on his Twitter page: "Dear Egyptians, Go back to your work on Sunday, work like never before and help Egypt become a developed country."

Though Tahrir Square was significantly less packed than in recent days, some protesters remained on Sunday morning. Some Egyptians have said they will continue protesting until, as one protester put it, "Egypt is ruled by a civil government, not a military one." On Sunday morning, soldiers maintained lines around the square.

In the immediate future, the military -- largely respected by Egyptians -- will have to grapple with guiding the country of more than 80 million people through the transition amid massive problems of unemployment and economic underdevelopment.

The African nation virtually shut down during the unrest, losing vital tourism dollars as well.

Some citizens who make their living off foreign tourists expressed anger. Businessmen near the famed Pyramids said about 50,000 people are employed in the tourism industry.

"Young boys 17 years old and 18 years old, they want to say, 'We are hungry, we want to eat, we want to work,'" one businessman, Ayman el Myonir, said Saturday.

As thousands reveled in their revolution, the nation's newly appointed military caretakers laid out priorities Saturday geared at establishing stability, though they revealed little to elucidate the future.

The Armed Forces Supreme Council said it was committed to a democratic process resulting in civilian rule, but urged respect for the reviled police forces that had clashed brutally with protesters in the early days of the uprising.

"The armed forces council calls on the people to cooperate with the policemen," Lt. Gen. Sami Anan, who some see as a potential presidential candidate, said on state television. "We ask our policemen to adhere to their slogan: Police is at the people's service."

It was unclear whether the statement signaled a return of the police security apparatus, which was noticeably absent from the streets after the violent clashes and the deployment of the army.

Patrons at a coffee shop in central Cairo said they now feel free to speak honestly about Egypt's political problems.

"I am happy and sad," said one customer named Fateh. "I am sad because this is the president who carried us through wars and tough times."

He said the turning point came when Mubarak supporters -- some of whom wielded whips -- rode horses and camels into the Tahrir Square crowd.

Anan, the armed forces chief of staff, said Egypt would still honor international treaties and commitments -- a statement perhaps aimed at calming a jittery Israel that has quietly watched dramatic change unfold in its Arab ally.

"Egypt is a country of institutions and it honors its legal obligations," Sameh Shoukry, Egyptian ambassador to the United States, told CNN's Wolf Blitzer on Saturday. The revolution is something "all Egyptians are proud of," the diplomat said.

Egypt and Israel signed a peace treaty in 1979. On Saturday, Israelis welcomed the Egyptian statement. Defense Minister Ehud Barak spoke on the phone with his Egyptian counterpart Hussein Tantawi, who heads the supreme council, the Israeli Defense Ministry said.

But as thousands of people still celebrated on the streets, the army's first statement since Mubarak's departure did little to spell out how long Egypt would remain under military rule.

"They want to see structural change," Parag Khanna of the Global Governance Initiative told CNN Saturday. "They want to see a change in the constitution. They want to see democracy. That speech did not tell them any of those things."

A marble memorial was being erected to remember those who died in the uprising. Human Rights Watch has documented 302 deaths, a number the monitoring group called conservative.

Egypt's constitution allows for only two scenarios if a head of state to relinquish power. The first stipulates that if the president has to step aside temporarily, the vice president steps into the top role. That is what Mubarak's regime briefly orchestrated Thursday.

If the office of the president is vacated or the president becomes permanently disabled, the constitution states that the parliamentary speaker is to assume the role until new elections can be held. Those elections, in turn, must occur within 60 days.

But Mubarak's regime put all power in the hands of the military -- which, in effect, rendered the constitution inoperable.

Anan, who serves as spokesman for the Armed Forces Supreme Council, said Saturday the current government would remain in place until a new one could be formed.

Several high-ranking government officials -- including the former prime minister and interior minister -- were facing lawsuits and were barred from traveling out of the country, state television reported, citing a judiciary source.

But some analysts were sounding the alarm over the takeover by the military, which has suddenly become accountable for the nation. Analysts with Stratfor, a global intelligence company, said Egypt had essentially experienced a coup.

"Egypt is returning to the 1952 model of ruling the state via a council of army officers," the Stratfor statement said. "The question now is to what extent the military elite will share power with its civilian counterparts."

But even as officials hash out the details of Egypt's murky political future, public demands for change rippled throughout the region.

In the Yemeni capital of Sanaa, protesters chanted Saturday: "Yesterday Tunisia, today Egypt -- tomorrow Yemen will open the prison."

And in restive Algeria, anti-government protesters chanted "Change the power" on Saturday. But security forces clashed with the crowds Saturday in Algiers and detained roughly 100 protesters, according to the opposition Algerian League for Human Rights.