Egypt's Muslim Brotherhood, the once outlawed opposition party, says it is not seeking power and will not put forward a presidential candidate at the upcoming election.

The government of Hosni Mubarak, who was pushed out of office on Friday after 18 days of public protests, long repressed the group, rounded up its members and banned it from a formal role in politics.

As thousands of once protesters tackle the clean-up in Egypt's capital, the Brotherhood has praised the efforts of the military, who were handed power when Mr Mubarak fled office after 30-years of autocratic rule.

The group says it is at the service of the people and does not have any ruling aspirations.

"We support and value the sound direction that the Higher Military Council is taking on the way to transfer power peacefully to create a civilian government in line with the will of the people," it said in a statement.

But the Brotherhood did express demands including an end to the state of emergency that was used to stifle dissent, the dissolution of parliament after last year's rigged elections, free and fair votes and the freeing of political prisoners.

It also called for freedom to create political parties and charges for those who had been involved in corruption over the years.

The US had expressed concern about the group's "anti-American" rhetoric and president Barack Obama says the group lacks majority support.

Meanwhile, in Cairo's Tahrir Square, instead of the previous night's wild celebrations, hundreds put on gloves and surgical masks and began cleaning up and removing the barricades.

Many spoke of the symbolism of beginning the rebuilding of their nation.

Police have reappeared in the centre of the city and businesses and restaurants are reopening.

The military has made yet another public statement promising to lift emergency law and steer the country towards democratic elections.

Some are sceptical but most appear to take them at their word.

Israeli prime minister Benjamin Netanyahu has welcomed the Egyptian military's renewed commitment to the peace treaty between their countries.

In one of the military's first acts since taking control, a senior officer said in a televised statement that Egypt would continue to observe all international treaties.

Israel watched warily throughout the weeks of protests in Egypt, fearing Islamic militants would use the instability to take power and overturn their 1979 peace treaty.

"The longstanding peace treaty between Israel and Egypt has greatly contributed to both countries and is the cornerstone for peace and stability in the entire Middle East," Mr Netanyahu said in a statement.

- ABC/Reuters