Thousands of Egyptians protested against President Mohammed Mursi after the assembly pushed through approval of a new constitution in a bid to end a crisis his newly expanded powers.
Mr Mursi said the decree halting court challenges to his decisions, was "for an exceptional stage" and aimed to speed up the democratic transition.
The move sparked eight days of protests and violence by Egyptians calling him a new dictator.
Mr Mursi told state television that the decree "will end as soon as the people vote on a constitution and insisted there "is no place for dictatorship."
Thousands packed Tahrir and took to the streets in Alexandria and cities on the Suez Canal, in the Nile Delta and south of Cairo, responding to opposition calls for a big turnout.
The opposition which has struggled to compete with well-organised Islamists has been drawn together and reinvigorated by the crisis.
Tens of thousands had also protested on Tuesday, showing the breadth of public anger.
Protesters said they would push for a No vote in a referendum, which could happen as early as mid-December. If approved, it would immediately cancel the president's decree.
In the Cairo mosque where Mr Mursi said Friday prayers, some opponents chanted against him but backers quickly surrounded him shouting in support, journalists and a security source said.
Thousands of Mursi supporters also turned out in Alexandria.
The referendum on the constitution is a gamble based on the Islamists' belief they can mobilise voters again after winning all the elections since Mubarak was overthrown in February 2011.
The assembly concluded the vote after a session that lasted 19 hours.
It approved all articles including presidential powers, the status of Islam, the military's role and the extent to which human rights will be respected in the post-Mubarak era.
The final draft contains historic changes to Egypt's system of government.
The president's term has been limited by the constitution to eight years.
It also introduces a degree of oversight over the military establishment - though not enough for critics.
Two people have been killed and hundreds injured in the protests since last Thursday's decree, which deepened the divide between the newly empowered Islamists and their opponents.
Crisis threatens to derail signs of economic recovery
The crisis also threatens to derail some early signs of an economic recovery after two years of turmoil.
Egypt's benchmark stock index fell yesterday to a four-month low.
An alliance of Egyptian opposition groups pledged to keep up protests.
They said broader civil disobedience was possible to fight what it described as an attempt to "kidnap Egypt from its people."
Eleven Egyptian newspapers plan not to publish on Tuesday to protest Mr Mursi's decree.
Three privately owned satellite channels have vowed they would not broadcast on Wednesday in protest.