After a week of opposition protests against Mr Morsi, his supporters in the Muslim Brotherhood came out in force.
They shouted slogans calling for the implementation of Sharia Law and defending Mr Morsi against claims he is grabbed the powers of a dictator.
Critics say the proposed constitution expands the role of Islam in public life and could be used to crack down on free speech.
But Muslim Brotherhood supporters say those who do not like will have their chance to vote against it and should accept Egypt's new democracy.
The crowds flooded the squares and large avenues near Cairo University, led by members of the Muslim Brotherhood, on whose ticket Mr Morsi ran for office, and by hardline Salafists, causing traffic jams in the capital.
"We want this phase to end. We want a constitution. If people don't like the constitution, let them say so through the ballot boxes," one protester said on Saturday.
Others chanted: "The people want the implementation of God's law."
"We are here to support the decisions of Dr Mohamed Morsi; we support him because those decisions were a part of the revolutionary demands," said Hend Abdellateef.
Veiled women ululated among the crowd, sprinkled with Egyptian and Saudi flags and posters of Mr Morsi, with banners reading: "Together (with Morsi) to save the revolution".
"There are people who want instability. There needs to be a constitution for there to be stability," said Khaled, one of the demonstrators, referring to anti-Morsi protesters.
Pro-Morsi protests were also staged in the Mediterranean city of Alexandria and the central Egyptian province of Assiut.
In Cairo, one demonstrator died and 24 others were injured when a tree fell near the main stage near the university.
The Muslim Brotherhood and their supporters have branded the opposition enemies of the revolution that toppled long-time dictator Hosni Mubarak in 2011.
Cairo's witnessed a week of opposition protests, and now the Muslim Brotherhood have answered that challenge.
While the opposition has accused their president of claiming the powers of a pharaoh, these people say he's just been trying to protect the revolution - to fend off challenges from judges loyal to the old Mubarak regime.
They point out Egyptians will be able to vote on the constitution in a referendum.
While human rights activists have raised concerns about some of the constitution's provisions, the Brotherhood says it will all be up to the new democracy in Egypt.
Middle East correspondent Matt Brown in Cairo
Across the Nile River, hundreds of protesters camping out in Tahrir Square since Mr Morsi issued a decree assuming sweeping powers were joined by more demonstrators throughout the day.
The National Rescue Front - a coalition of opponents led by dissident former UN nuclear watchdog chief Mohamed ElBaradei, ex-Arab League chief Amr Mussa and former presidential candidate Hamdeen Sabbahi - has called on the decree's opponents to keep up the pressure.
It said Egyptians should "reject the illegitimate" decree and the "void" draft constitution, and stressed the public's right "to use any peaceful method to protest including a general strike and civil disobedience."
The crisis was sparked when Mr Morsi issued the decree on November 22 giving himself sweeping powers and placing his decisions beyond judicial review, provoking mass protests and a judges' strike.
His decree prevented the top legal body the Supreme Constitutional Court from potentially dissolving the Islamist-run constituent assembly, in a ruling it was to make on Sunday on the body's legality.
"Rushing through a draft while serious concerns about key rights protections remain unaddressed will create huge problems," said Joe Stork of Human Rights Watch.
Amnesty International said the draft "raises concerns about Egypt's commitment to human rights treaties," specifically ignoring "the rights of women (and) restricting freedom of expression in the name of religion."
In an interview broadcast on Thursday night, Mr Morsi again stressed that his new powers would expire once the constitution was ratified, a point Islamist supporters have repeatedly made in his favour.
The Brotherhood and the secular-leaning opposition had stood side by side in Tahrir Square in 2011 as they fought to bring down Mubarak and his regime.
But since Mubarak's downfall in February 2011, the Islamist movement has been accused of monopolising power.