Television pictures of Tahrir Square show enormous crowds of people chanting the Egyptian national anthem and calling for Mubarak to go.
Protesters have been flooding into the centre of Cairo since the end of Friday's Islamic prayers. Soldiers have set up checkpoints at entrances to the square, apparently to stop provocateurs infiltrating the protests. Long queues of people are still waiting to join the demonstration.
So far, there have been no reports of violence.
Defence Minister Hussein Tantawi, accompanied by senior army officials, addressed the crowd in Tahrir Square on Friday morning. He said that Mubarak had already agreed not to run for re-election, and called on opposition groups to negotiate with the government.
Protest movements have designated Friday as the deadline for Mubarak to leave power.
The US is pushing for Mubarak to hand over power to a transitional government led by Vice President Omar Suleiman and backed by the Egyptian army, according to a report in the New York Times.
The proposal, which is said to be one of several scenarios under discussion by senior US and Egyptian officials, would require the interim leadership to begin constitutional reform immediately. Another key aim is free and fair elections in September, in which a broad range of opposition groups, including the banned Muslim Brotherhood, would be invited to participate.
The Muslim Brotherhood, Egypt's largest opposition movement, said on Friday that it was ready to engage in dialogue - but ony if Mubarak steps down. His resignation is the Brotherhood's "single demand", chairman Mohammed Badie told Al Jazeera television.
The movement has said that it does not intend to enter a presidential candidate in September's elections.
Iran's supreme leader Ayatollah Ali Khamenei called for an Islamic regime to replace Mubarak, who he dismissed as the "servant" of Israel and the US. Egyptians should not back down until they establish "a popular regime based on religion", Khamenei said in his Friday sermon in Tehran.