Mohamed ElBaradei, the former head of the U.N. nuclear watchdog, and former presidential candidates Hamdeen Sabbahi and Amr Moussa promised to spend the night in the square, the Egypt Independent reported.
ElBaradei said via Twitter Morsi "and his constituent assembly are currently staging a coup against democracy. Regime legitimacy fast eroding," Ahram Online reported
The Constitutional Declaration was passed early Friday, despite walkouts by liberal and leftist lawmakers. The quick vote on the constitution, which caught many by surprise, was the topic of Friday prayers in Tahrir Square, witnesses told Ahram Online.
Protesters chanted "leave" and "the people want to bring down the regime," as they were finishing Friday prayers, witnesses said.
A sheik leading prayers in the square told protesters the Muslim Brotherhood and the Salafists tainted Islamic Sharia law and accused the once-outlawed Brotherhood of taking advantage of the "blood of the martyrs" of last year's revolution that culminated in the overthrow of President Hosni Mubarak to secure power.
ElBaradei said the constitution "belongs in the garbage can of history" in an interview with Egyptian private television channel al-Nahra Thursday.
Security forces built barricades around Tahrir Square before the protests, Ahram Online said. Protesters at entrance checkpoints clogged the streets as they were searched before being allowed to enter.
Hossam el-Gheriany, head of the assembly, confirmed passage of the document early Friday after a marathon session, Ahram Online said. He said he would "call the president today [Friday] at a reasonable hour to inform him that the assembly has finished its task and the project of the constitution is completed."
Morsi said in a televised speech Thursday, there is "no place for a dictatorship," in an attempt to reassure the country.
Morsi said the powers he assumed in a decree issued last week were "for an exceptional stage," and would end "as the people vote on the constitution."
The decree exempts all of Morsi's decisions from judicial oversight until the new constitution is ratified and a new Parliament elected. Since he issued the declaration, mass protests by opposition forces and a judges strike spread across the nation, Egypt Independent said.
Morsi said if the final constitutional draft is rejected by voters, then a new Constituent Assembly would be formed to write a new draft.
A referendum must be conducted within 30 days.
The draft Constitution defines Egypt as a Muslim nation and says, for the first time in the republic's history, Parliament must consult clerics at the revered Sunni al-Azhar Mosque, built in 970 in Islamic Cairo, on legislation "related to Islamic Sharia," the Los Angeles Times said.