Tens of thousands have gathered in central Cairo for a seventh day of protest, calling for a general strike.
Police have been ordered back to the streets, to positions they abandoned on Friday, but it is not clear whether they are returning to central Cairo.
The demonstrators are also planning a huge march to take place on Tuesday.
Protesters want President Hosni Mubarak to step down after 30 years in power. He has promised political reform and has now announced a new cabinet.
The state TV announcement said Interior Minister Habib al-Adly, who correspondents say is widely despised by protesters, had been replaced.
The president has ordered his new Prime Minister, Ahmed Shafiq, to push through democratic reforms and create new jobs.
Correspondents say all the signs continue to suggest that the only change the protesters will settle for is Mr Mubarak’s removal from office.
Policeman directing traffic Some police have been seen directing traffic
Meanwhile, Moodys Investor Services has downgraded Egypt’s bond rating and changed its outlook from stable to negative, following a similar move by Fitch Ratings last week. Both cited the political crisis.
‘Protest of millions’
But there were signs of disagreement within the opposition, with the largest group, the Muslim Brotherhood, appearing to go back on its endorsement of leading figure Mohamed ElBaradei as a negotiator with Mr Mubarak.
As demonstrations enter their seventh day, correspondents say there are at least 50,000 people on Tahrir Square in the centre of the city.
At the scene
Kevin Connolly BBC News, Cairo
On the seventh day of the crisis which will help define Egypt’s future, the extraordinary is beginning to feel ordinary. The now familiar rhythms of a day of protest are re-establishing themselves.
Demonstrators remain on Tahrir Square, their strength hard to assess as their numbers fluctuate over the course of the day.
The role of the army remains enigmatic. Troops are on the street and military checkpoints have been playing a more assertive role today in controlling traffic crossing the bridges over the Nile.
The soldiers see themselves as a force for stability and while some of their armoured vehicles are daubed with graffiti that reads “Down with Mubarak” it’s also true that the very act of preserving order helps the old regime to maintain its grip on power.
The opposition is declaring a general strike and talks of bringing a million people onto the streets tomorrow but it’s far from clear that they have the coherent structure to keep sustained pressure focused on the Mubarak administration.
One possible outcome of this remains a Hosni Mubarak who will be re-booted rather than booted out.
The BBC’s Jim Muir in Cairo says the military, who have cordoned off the square with tanks, are very relaxed and letting people come and go.
Elsewhere the streets are busy and things appear to be returning to normal, with some police returning and seen directing traffic.
But there are no riot police, and our correspondent says the government is being quite clever in keeping the unpopular police force out of contact with the protesters.
There are plans for a “protest of the millions” march on Tuesday.
Our correspondent says this is an attempt to reinvigorate the movement, as many are wondering what to do next if Mr Mubarak stays in power, as he is showing every sign of doing.
Mr ElBaradei has been mandated by opposition groups to negotiate with the regime.
But a spokesman for the largest opposition group, the Muslim Brotherhood, appeared to reject this position.
“The people have not appointed Mohamed ElBaradei to become a spokesman of them,” Mohamed Morsy told the BBC.
“The Muslim Brotherhood is much stronger than Mohamed ElBaradei as a person. And we do not agree on he himself to become representing [sic] this movement, the movement is represented by itself, and it will come up with a committee… to make delegations with any government.”
Thousands have rallied in Alexandria, and there have also been sizeable demonstrations in Mansoura, Damanhour and Suez.
The unrest is having an impact on the Egyptian economy, beyond the closure of shops and businesses and the call for a general strike.
* Most populous Arab nation, with 84.5 million inhabitants
* Authoritarian President Hosni Mubarak has ruled for 30 years
* Protests against corruption, lack of democracy, inflation, unemployment
* Triggered by overthrow of President Zine al-Abidine Ben Ali of Tunisia
Many counties including the US, China and the Netherlands are evacuating their citizens, leading to chaotic scenes at Cairo airport as air traffic becomes congested and flights are cancelled or delayed.
Tourism is a vital sector in the Egyptian economy, accounting for about 5-6% of GDP.
International pressure is growing for some kind of resolution.
The White House says Mr Obama made a number of calls about the situation over the weekend to foreign leaders including Turkish Prime Minister Recep Tayyip Erdogan, King Abdullah of Saudi Arabia and British Prime Minister David Cameron.
The protests in Egypt are top of the agenda of a meeting of European Union foreign ministers in Brussels on Monday.
The unrest in Egypt follows the uprising in Tunisia which ousted President Zine al-Abidine Ben Ali two weeks ago after 23 years in power.