Hundreds of demonstrators in Port Said, Suez and Ismailia turned out against the decision within moments of Mursi's announcement late on Sunday that came after the death toll from protests and violence that erupted last week hit 49 people.
Most deaths were in Port Said, where 40 people were killed in just two days. Riots were sparked on Saturday when a court sentenced to death several people from the city in a case of deadly soccer violence last year. Mourners at Sunday's funerals in the port, where guns are common, turned their rage on Mursi.
The violence in Egyptian cities has now extended to a fifth day. Police again fired volleys of teargas at dozens of youths hurling stones early on Monday near Cairo's Tahrir Square, where opponents have camped for weeks to protest against Mursi, who they say betrayed the revolution that overthrew Hosni Mubarak two years ago.
"We want to bring down the regime and end the state that is run by the Muslim Brotherhood," said Ibrahim Eissa, a 26-year-old cook, protecting his face from teargas wafting towards him from police lines near Tahrir, the cauldron of the 2011 revolt.
Propelled to power in a June election by the Brotherhood, Mursi's presidency has lurched through a series of political crises and violent demonstrations, compounding his task of shoring up a teetering economy and preparing for a parliamentary election to cement the new democracy in a few months.
"The protection of the nation is the responsibility of everyone. We will confront any threat to its security with force and firmness within the remit of the law," Mursi said, offering condolences to families of victims in the canal zone cities.
Appealing to his opponents, the president called for a national dialogue on Monday at 6 p.m. (1600 GMT), inviting a range of Islamist allies as well as liberal, leftist and other opposition groups and individuals to discuss the crisis.
"WASTE OF TIME"
The main opposition National Salvation Front coalition said it would meet on Monday to discuss the offer. But some opponents have already suggested they do not expect much from the gathering, raising the prospect of poor attendance.
"Unless the president takes responsibility for the bloody events and pledges to form a government of national salvation and a balanced committee to amend the constitution, any dialogue will be a waste of time," Mohamed ElBaradei, a prominent politician who founded the Constitution Party, wrote on Twitter.
Hamdeen Sabahy, a firebrand leftist politician and presidential candidate who is another leading member of the Front, said he would not attend Monday's meeting "unless the bloodshed stops and the people's demands are met."
The response highlights Egypt's deeply polarized politics. Although Islamists have swept to victory in a parliamentary poll and presidential vote, the disparate opposition has been united by Mursi's bid late last year to expand is powers and fast-track a constitution with an Islamist hue through a referendum.
Mursi's opponents accuse him of listening only to his Islamist friends and reneging on a pledge to be a president for all Egyptians. Islamists say their rivals want to overthrow by undemocratic means Egypt's first freely elected leader.
The Front has distanced itself from the latest flare-ups but said Mursi should have acted far sooner to impose extra security measures that would have ended the violence and laid the blame for the escalation squarely on Mursi's shoulders.
"Of course we feel the president is missing the real problem on the ground, which is his own polices," spokesman Khaled Dawoud said. "His call to implement emergency law was an expected move given what is going on, namely thuggery and criminal actions."
Even in Tahrir Square, some protesters said the violence and the death toll in Port Said and other cities along the strategic international waterway meant there was little choice but to impose emergency law, though they, too, said the violence was Mursi's fault.
"They needed the state of emergency there because there is so much anger," said Mohamed Ahmed, 27, a protester walking briskly from a cloud of teargas spreading into Tahrir Square.
But activists in the three cities affected have pledged to defy the curfew that will start at 9 p.m. (1900 GMT) each evening and will last until 6 a.m. (0400 GMT).
Some opposition groups have also called for more protests on Monday, which marks the second anniversary of one of the bloodiest days in the revolution that erupted on January 25, 2011, and brought an end to Mubarak's iron rule 18 days later.
Rights activists also said Mursi's declaration was a backward step for Egypt, which was under emergency law for Mubarak's entire 30-year rule. His police used the sweeping arrest provisions to muzzle dissent and round up opponents, including members of the Brotherhood and even Mursi himself.
Heba Morayef of Human Rights Watch in Cairo said the police, still hated by many Egyptians for their heavy-handed tactics under Mubarak, would once again have the right to arrest people "purely because they look suspicious", undermining efforts to create a more efficient and respected police force.
"It is a classic knee-jerk reaction to think the emergency law will help bring security," she said. "It gives so much discretion to the Ministry of Interior that it ends up causing more abuse, which in turn causes more anger."