President Mohammed Morsi has said Egypt's new draft constitution will be put to a referendum on 15 December.
He made the announcement before the Islamist-dominated constituent assembly, which rushed to approve the document earlier in the week.
Both the draft constitution and a recent decree giving Mr Morsi sweeping new powers have prompted widespread protests by opponents of the president.
However, his Islamist supporters held their own demonstrations on Saturday.
After receiving a copy of the document, Mr Morsi called on "all Egyptians" to take part in the referendum, whether or not they agree with the draft.
"The world is looking at how Egyptians will build their institutions to establish their democratic system," the president added.
The BBC's Jon Leyne in Cairo that the two weeks until the ballot will be tense, as Egyptians prepare to vote not just on the constitution but also on the country's future.
The Supreme Constitutional Court, Egypt's highest judicial authority, is due to rule Sunday on the legitimacy of the constituent assembly. It is unclear whether a decision to disband it would affect plans for a vote, correspondents say.
'Struggle will continue'
The constituent assembly voted on and passed all 234 articles during a marathon session that began on Thursday and continued through the night.
Liberals, secularists and Christians walked out saying the changes were being forced through.
"Morsi put to referendum a draft constitution that undermines basic freedoms and violates universal values. The struggle will continue," key opposition figure Mohamed ElBaradei tweeted on Saturday.
If approved, the new text will overwrite all constitutional declarations - including Mr Morsi's decree issued on the 22 November - and a new parliament should be elected within 60 days.
Among the historic changes to Egypt's system of government, the draft limits a president to two four-year terms. It also introduces some civilian oversight of the military.
The draft keeps in place an article defining "principles of Sharia", or Islamic law, as the main source of legislation.
Earlier, tens of thousands of Islamist supporters of the president gathered outside Cairo university.
"The people support the president's decision!" they chanted, while a banner read: "The people want the implementation of God's law."
Mr Morsi's supporters point to the fact that he is Egypt's first freely elected president and argue that liberals and secularists do not represent the vast majority of Egyptians.
But the extent of Mr Morsi's new powers has raised fears that he might become a new dictator.
Under the recent decree, Mr Morsi's decisions cannot be revoked by any authority, including the judiciary, until the constitution has been ratified and a fresh parliamentary election held.
Senior judges have opposed the move, and opponents have held mass rallies across the country in the past week. Many anti-government activists remain camped out in Cairo's Tahrir Square.
UN Human Rights Commissioner Navi Pillay has written to the president, asking him to reconsider his decree and warning that "approving a constitution in these circumstances could be a deeply divisive move".