The military rulers who took over when Mubarak stepped down Friday and the caretaker government set as a top priority the restoration of security, which collapsed during the 18 days of protests that toppled the regime. The caretaker government held its first meeting since the president was ousted and before it began, workers removed a giant picture of Mubarak from the meeting room.
The protesters had been pressing the ruling military council, led by Defense Minister Hussein Tantawi, to immediately move forward with the transition by appointing a presidential council, dissolving the parliament and releasing political prisoners.
"They have definitely started to offer us what we wanted," said activist Sally Touma, reflecting a mix of caution and optimism among the protesters. Thousands have remained in Cairo's central Tahrir Square to demand immediate steps by the council such as the repeal of repressive emergency laws that give police broad power.
The suspension of the constitution effectively puts Egypt under martial law - where the military makes the laws and enforces them in military tribunals. The ruling council is expected to clarify the issue in upcoming statements and the role of civilian courts remains unclear.
Judge Hisham Bastawisi, a reformist judge, said the latest measures "should open the door for free formation of political parties and open the way for any Egyptian to run for presidential elections" which the constitutional amendments are expected to do.
Hossam Bahgat, director of the non-governmental Egyptian Initiative for Personal Rights, said the military's steps were positive but warned that Egypt was on uncharted legal ground.
"In the absence of a constitution, we have entered a sort of 'twilight zone' in terms of rules, so we are concerned," he said. "We are clearly monitoring the situation and will attempt to influence the transitional phase so as to respect human rights."
The ruling council said it will run the country for six months, or until presidential and parliament elections can be held. It said it was forming a committee to amend the constitution and set the rules for a popular referendum to endorse the amendments.
Both the lower and upper houses of parliament are being dissolved. The last parliamentary elections in November and December were heavily rigged by the ruling party, virtually shutting out opposition representation.
The caretaker Cabinet, which was appointed by Mubarak shortly after the pro-democracy protests began on Jan. 25, will remain in place until a new Cabinet is formed - a step that is not expected to happen until after elections. The ruling council reiterated that it would abide by all of Egypt's international treaties agreed in the Mubarak era, most importantly the 1979 peace treaty with Israel.
"Our concern now in the Cabinet is security, to bring security back to the Egyptian citizen," Prime Minister Ahmed Shafiq told a news conference after the Cabinet meeting.
Shafiq said the military would decide whether Omar Suleiman, who was appointed vice president by Mubarak in a failed attempt to appease protesters, would play some role in Egypt's transition.
"He might fill an important position in the coming era," the prime minister said.
He also denied rumors that Mubarak had fled to the United Arab Emirates, saying the former president remained in the Red Sea resort of Sharm el-Sheikh. He went there just hours after stepping down.
"In a country like Egypt, with a pharaonic legacy, having no president and no head of state is not easy," said Amr el-Shobaky, a member of the Committee of Wise Men - a self-appointed group of prominent figures who are allied with the protesters.
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 at the start of the protests that killed many demonstrators.
"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.
The 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 at least two banks as Egyptians emboldened by the autocrat'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, the crowds of protesters were thinning out and traffic moved through the area for the first time. Many local residents shouted at the protesters that it was time to go.
The Armed Forces Supreme Council is now the official ruler of Egypt after Mubarak handed it power. It consists of the commanders of each military branch, the chief of staff and Defense Minister Tantawi, who is now the top leader of Egypt.
The military took power after pleas from protesters, and it has promised to ensure democratic change. The institution, however, was tightly bound to Mubarak's ruling system, and it has substantial economic interests that it will likely seek to preserve.
Egypt's state news agency said banks will be closed Monday due to strikes and Tuesday for a public holiday.
Associated Press writer Maggie Michael contributed to this report.