Tens of thousands are protesting in central Cairo for a seventh day, defying the start of a new curfew and calling for a general strike.
President Hosni Mubarak has now announced a new cabinet that removes Interior Minister Habib al-Adly, who is widely despised by protesters.
They want the president to step down after 30 years in power and are planning a huge march for Tuesday.
Police who abandoned their posts on Friday are back in some parts of Cairo.
Mr Mubarak has ordered new Prime Minister Ahmed Shafiq to push through democratic reforms and create new jobs.
There are few major changes in the new cabinet line-up, with Foreign Minister Ahmed Abul Gheit and Defence Minister Gen Mohamed Hussein Tantaw both keeping their posts.
A number of businessmen holding economic posts have been removed. Some Egyptians have resented the influence of the tycoons.
However, correspondents say all the signs continue to suggest that the only change the protesters will settle for is Mr Mubarak's removal from office.
Meanwhile, Moody's 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'
As demonstrations enter their seventh day, correspondents say there are at least 50,000 people on Tahrir Square in the centre of the city.
Many protesters dismissed the new cabinet appointments.
One, Rifat Ressat, told Agence France-Presse: "We want a complete change of government, with a civilian authority."
But he did welcome the replacement of Interior Minister Adly, who he said was "responsible for all the violence".
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.
There have been some 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.
A spokesman for the Muslim Brotherhood, Mohamed Morsy, told the BBC: "The people have not appointed Mohamed ElBaradei to become a spokesman of them.
"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.
Many countries 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.
In the strongest language yet, both US President Barack Obama and his Secretary of State Hillary Clinton talked about the need for an "orderly transition" to a democratic future for Egypt.
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.