They also met with representatives of the broad-based youth movement that brought down the government after an 18-day uprising that transfixed the world.
The caretaker government, backed by the military, said restoring security was a top priority even as labor unrest reflected one of the many challenges of steering the Arab world's biggest nation toward stability and democracy.
On Sunday, prominent activist Wael Ghonim posted on a Facebook page he manages notes from a meeting between members of the military council and youth representatives, which he described as encouraging.
The military defended the caretaker government, stocked with Mubarak loyalists, as necessary for now in the interests of stability but pledged to soon change it, said Ghonim and another protester, Amr Salama, in the statement.
"They said they will go after corrupt people no matter what their position current or previous," the statement added. Amendments to the much reviled constitution will be prepared by an independent committee over the next 10 days and then presented for approval in a popular referendum to be held in two months, they said.
The military also encouraged the youth to consider forming political parties - something very difficult to do under the old system - and pledged to meet with them regularly.
"We felt a sincere desire to protect the gains of the revolution and an unprecedented respect for the right of young Egyptians to express their opinions," Ghonim said.
Even amid the efforts to build a new system, Egypt's upheaval has splintered into a host of smaller grievances, the inevitable outcome of emboldened citizens feeling free to speak up, most for the first time.
They even included about 2,000 police, widely hated for brutality and corruption under Mubarak, who marched to the Interior Ministry to demand better pay and conditions. They passed through the protest camp at Tahrir Square, where demonstrators hurled insults, calling them "pigs" and "dogs."
Egypt's state news agency announced banks would be closed Monday due to strikes and again Tuesday for a public holiday. Dozens of employees protested against alleged corruption at the state television building, which broadcast pro-Mubarak messages during the massive demonstrations against his rule.
The caretaker government met for the first time, and employees removed a huge frame photograph of Mubarak from the meeting room before they convened.
The crowds in the protest encampment that became a symbol of defiance against the government thinned out Sunday - the first working day since the regime fell. Traffic flowed through downtown area for the first time in weeks. Troops cleared most of the makeshift tents and scuffled with holdout activists.
The protesters have 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 parliament and releasing political prisoners. Thousands have remained in Tahrir Square and some want to keep up the pressure for immediate steps, including repeal of repressive emergency laws that give police broad power.
As Egypt embarked on its new path - one of great hope but also deep uncertainty - the impact of its historic revolt and an earlier uprising in Tunisia was evident in a region where democratic reform has made few inroads.
Yemeni police clashed Sunday with protesters seeking the ouster of the U.S.-backed president, and opposition groups planned a rally in Bahrain on Monday. Demonstrators have also pushed for change in Jordan and Algeria, inspired by the popular revolt centered in downtown Cairo.
The 18-member Supreme Council of the Armed Forces allayed some concerns by dismissing the legislature, packed with Mubarak loyalists, and sidelining the constitution, used by Mubarak to buttress his rule. Activists said they would closely watch the military to ensure it does not abuse its unchecked power - something that is clearly starting to make some uneasy.
The council "believes that human freedom, the rule of law, support for the value of equality, pluralistic democracy, social justice, and the uprooting of corruption are the bases for the legitimacy of any system of governance that will lead the country in the upcoming period," the Council said in a statement.
"They have definitely started to offer us what we wanted," said activist Sally Touma, who also wants the release of political prisoners and repeal of an emergency law that grants wide powers to police.
The military council, which has issued a stream of communiques since taking power, said parliamentary and presidential elections will be held, but did not set a timetable. It said it will run the country for six months, or until elections can be held.
It said it will represent Egypt in all internal and external affairs and proclaimed the right to set temporary laws. It was expected to clarify the scope of its legal authority as the complex transition unfolds and the role of the judiciary remains unclear.
It said it was forming a committee to amend the constitution and set rules for a popular referendum to endorse the amendments.
Protesters are demanding that the constitution be amended to impose term limits on the president, open up competition for the presidency, and remove restrictions on creating political parties. Others want an entirely new constitution.
Judge Hisham Bastawisi, a reformist judge, said the military measures "should open the door for free formation of political parties and open the way for any Egyptian to run for presidential elections."
Hossam Bahgat, director of the non-governmental Egyptian Initiative for Personal Rights, said the 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."
Both the lower and upper houses of parliament are being dissolved. The last parliamentary elections in November and December were marked by allegations of fraud by the ruling party, which was accused of virtually shutting out the opposition.
The military council includes the chief of staff and commanders of each branch of the armed forces. It took power after protesters' pleas, and promised reform. The institution, however, was tightly bound to Mubarak's ruling system, and it has substantial economic interests that it will likely seek to preserve.
The caretaker Cabinet, 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 expected to happen after elections.
"Our concern now ... is security, to bring security back to the Egyptian citizen," Prime Minister Ahmed Shafiq said Sunday after the Cabinet met for the first time since Mubarak was ousted.
Security remains thin in Cairo, more than two weeks after police withdrew following clashes with protesters. Some have returned, but many say they might quit, citing humiliation and ill-treatment from people in the street. Others are on leave. Military police are directing traffic and filling in some of the gaps.
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 reports that Mubarak had fled to Germany or the United Arab Emirates, saying the former president remained in the Red Sea resort of Sharm el-Sheikh, where he went soon after stepping down.
Egyptians became accustomed to scenes of police beating protesters in the early days of the uprising, but on Sunday it was the police who were demonstrating. A large group marched through Tahrir Square to demand higher wages, and sought to absolve themselves of responsibility for the attempted crackdown in the early days of the Egyptian uprising.
"You have done this inhuman act," a protester said.
Said Abdul-Rahim, a low-ranking officer, broke into 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. "
Police officers scuffled with soldiers outside the Interior Ministry, and some troops fired gunshots in the air.
"This is our ministry," the police shouted. "The people and the police are one hand," they chanted, using an expression for unity. They complained their monthly salaries are 500-600 Egyptian pounds ($85-$100), and soldiers are far better compensated.
Interior Minister Mahmoud Wagdy emerged from the building to talk to the police through a megaphone.
"Give me a chance," he said. Later, the ministry said it was doubling the pay of low-ranking police.
Some police had been accused of stripping off their uniforms and joining gangs of thugs who attacked protesters at the height of the uprising.
There were also protests by workers at a ceramic factory, a textile factory and a port on the Mediterranean coast as Egyptians sought to improve their lot in a country where poverty and other challenges will take years to address.
Outside the headquarters of one of Egypt's major public banks, several hundred employees protested against alleged corruption by the bank manager, a government-appointed official. Protester Yasmine Haidar said newly appointed advisers to the manager had salaries nearly 70 times higher than her monthly $190.
"After the president left, we need the rest to leave behind him," she said. "The heads of all the rotten fish should be cut."
The five top officials at the bank left the building because employees had stopped working.
Meanwhile, in Tahrir Square, soldiers tried to convince the few remaining protesters to clear their tents and blankets.
An army vehicle drove through the square, broadcasting the military's announcement that it would dissolve parliament and suspend the constitution. Soldiers got out of the car to converse with protesters about the ruling council's plans. Some people clapped and cheered.
Some protesters were unsatisfied, and gathered with a wooden cross and a copy of the Quran.
"The government is still in place. The corruption is still here. Emergency laws are still here," said Mohammed Ahmed, an accountant. "When it is a civil state and we have a parliamentary system and political detainees are released, then we go."