In an address on state television Sunday evening, Morsi said the emergency measures would come into effect in the provinces of Port Said, Suez and Ismailiya "for 30 days starting at midnight (2200 GMT Sunday)".
Curfews would be imposed on the same three provinces from 9:00 pm until 6:00 am, he added -- and he warned he would take further steps to confront threats to Egypt's security if need be.
But Morsi also invited opposition politicians for talks Monday in a bid to bridge the growing political gulf in the country.
Morsi acted after a second day of rioting rocked Port Said Sunday, sparked by death sentences handed down by a court on Saturday against some of those convicted over deadly football riots last year.
Sunday's violence left another six people dead and more than 460 injured, according to medics.
Crowds attempted to storm three police stations in the Suez Canal city, while others looted and torched an army social club, security officials said.
The latest casualties, among them a teenager shot in the chest, added to the toll of 31 people including two anti-riot police killed in the city on Saturday.
Unrest also erupted on Sunday in Suez, another canal city, where protesters surrounded a police station, lobbed Molotov cocktails at security forces and blocked the road leading to the capital, security officials said.
In Cairo, police clashed with protesters who accuse Morsi of betraying the goals of the revolution that ousted Hosni Mubarak two years ago, highlighting deep political divisions in the country now ruled by Islamists.
Clashes near Tahrir Square -- symbolic heart of the 2011 uprising that toppled Mubarak -- continued sporadically during the day and into Sunday evening, witnesses said.
The US and British embassies, located just minutes from Tahrir Square, closed their services to the public for the day.
Morsi warned that he was ready to take further measures unless there was an end to the deadly unrest that has swept Egypt since Friday, when protests to mark the second anniversary of the anti-Mubarak revolt turned violent.
"If I must I will do much more for the sake of Egypt. This is my duty and I will not hesitate," the president said.
"There is no alternative to dialogue"
A few hundred people took to the streets of Ismailiya just after Morsi's announcement and clashed with police, an AFP correspondent said. A medical source said six people had been injured.
Morsi in his address also held out an olive branch to the opposition and political leaders across Egypt, inviting them for talks on Monday.
"There is no alternative to dialogue," he said.
A statement by his office said the leaders of the National Salvation Front, the main coalition of parties and movements opposing the ruling Islamists, were among those invited to the talks at 1600 GMT Monday at the presidential palace.
The National Salvation Front, led by Nobel peace laureate Mohammed ElBaradei, former Arab League boss Amr Mussa and leftist politician Hamdeen Sabbahi, has warned it will "not participate" in upcoming parliamentary polls unless the causes of the violence are addressed.
The rioting in Port Said began on Saturday after a Cairo court handed down death sentences on 21 supporters of the local football club, Al-Masry, in the wake of football violence last February that left 74 people dead.
Everyone had to respect the verdicts, Morsi insisted, condemning the violence as "a violation of the law and a violation of the revolution".
Earlier Sunday, residents of Port Said buried those killed the previous day. Their bodies, wrapped in white shrouds, were carried in open coffins by a sea of mourners along the city's main avenue.
"Our city is being hit by the interior ministry!" and "Down with Brotherhood rule!" chanted the crowd, referring to the Muslim Brotherhood from which Morsi draws his main support.
A brief burst of gunfire sent mourners scattering amid chaotic scenes, which later degenerated into fresh rioting.
Egypt was under a state of emergency for more than three decades in the wake of the assassination of president Anwar Sadat in 1981 and until May last year, a month before Morsi was elected.
Ending the state of emergency -- which allowed authorities to detain people without charge and try them in emergency security courts -- was a key demand of protesters who toppled Mubarak in 2011.