The army's pledge on Monday not to use force against demonstrators emboldened Egyptians to push for the biggest shake-up of the political system since 1952 when army officers deposed King Farouk.
More than 200,000 Egyptians crowded into Tahrir Square in central Cairo and 20,000 marched in the eastern city of Suez. Demonstrations were held in Alexandria on the north coast, Ismailia and cities in the Nile Delta such as Tanta, Mansoura and Mahalla el-Kubra.
Across the country the numbers expressing their anger with Mubarak and his ministers have hit the million mark that activists wanted, according to a Reuters estimate.
"Mubarak wake up, today is the last day," they shouted in Alexandria.
The scenes in Tahrir (Liberation) Square, which has become a rallying point for protests over poverty, repression and corruption, were in sharp contrast to Friday when police beat, teargassed and sprayed water cannon on protesters.
"He goes, we are not going," chanted a crowd of men, women and children as a military helicopter hovered over the sea of people, many waving Egyptian flags and banners.
"Mubarak you coward, you agent of the United States."
Soldiers, some perched atop armoured vehicles defaced with anti-Mubarak graffiti, smiled and nodded as protesters punched the air and shouted: "The people and the army are hand in hand ... down, down Hosni Mubarak."
A couple of hundred pro-Mubarak supporters gathered near the Foreign Ministry, a little distance from Tahrir Square. "Yes to Mubarak, No to Elbaradei, No to spies in Egypt," they shouted, their small number serving to highlight his unpopularity.
There had been talk the anti-Mubarak rally would march on the presidential palace on Tuesday but by early afternoon the crowd showed no sign it was ready to move on.
Initially unorganised, the protests against Mubarak are gradually coalescing into a loose reformist movement encompassing many sections of Egyptian society.
Young unemployed mixed with members of the Islamist movement the Muslim Brotherhood, and the urban poor held hands in solidarity with doctors and teachers.
"We are calling for the overthrow of the regime. We have one goal, and that is to remove Hosni, nothing else. Our need to step in and form coalitions and committees to propose a new administration," said Ahmed Abdelmoneim, 25, a computer engineer.
Mubarak has not addressed the nation since Friday, when he sacked his cabinet. On Monday, it was his newly appointed vice president, Omar Suleiman, who announced a call for dialogue with all political forces. Protesters scent victory.
"The revolution won't accept Omar Suleiman, even for a transitional period. We went a new democratic leader," said Mohamed Saber, a member of the Muslim Brotherhood.
"We are very patient, we can stay here a long time ... For the last 30 years this regime brought the worst out of the people. Now everyone is speaking out. Before everyone was negative and passive," said Mahmoud Ali, 42, a civil servant.
What will come after Mubarak if he steps down is not so clear. Egypt's opposition has been fragmented and weakened under Mubarak. The Muslim Brotherhood has the biggest grassroots network with its health and other social charity projects.
The group, banned from politics under Mubarak, says it wants an Islamic, pluralistic and democratic state.
"Our country has many people capable of being president," said Essam Kamel, 48, a lawyer, although he said he did not want Nobel Peace Prize laureate Mohamed ElBaradei, who has said he was ready to take on a role in the transition.
But Kamel added: "We are Muslims, but we don't need an Islamic government."