Ahead of Morsi's speech Wednesday, deadly clashes broke out in Mansoura, where a Health Ministry spokesman said two people were killed and 170 injured in fighting between supporters and opponents of the government, the BBC reported.
Morsi, leader of the Muslim Brotherhood, became Egypt's first Islamist president June 30, 2012, after winning an election considered free and fair. His first year in office has been marked by political unrest and a tanking economy.
In his 2-hour televised speech Wednesday, Morsi defended his first year, admitting mistakes and promising reforms to address them. He apologized for fuel shortages that led to long lines at gas stations and for failure to involve the nation's youth enough.
"I was right in some cases, and wrong in other cases," he said. "I have discovered after a year in charge that for the revolution to achieve its goals, it needs radical measures."
Then the speech took on a more condemning tone, the BBC said.
"I took responsibility for a country mired in corruption and was faced with a war to make me fail," he said, naming several officials he thought wanted to "turn the clock back" to when longtime, former President Hosni Mubarak was in office.
"Political polarization and conflict has reached a stage that threatens our nascent democratic experience and threatens to put the whole nation in a state of paralysis and chaos," he warned. "The enemies of Egypt have not spared effort in trying to sabotage the democratic experience."
He challenged those who oppose his government to "enter elections if you want to change the government" and criticized them for refusing to participate in a national dialogue.
The president said he would invite party leaders to meet to select a chairman for a committee tasked with preparing amendments to the constitution approved by referendum last year amid protests by numerous groups. He also said he was forming a committee of leading public figures to promote national reconciliation.
Ahead of his speech, anti-government supporters gathered in Cairo's Tahrir Square and outside the Defense Ministry, the BBC said.
In Mansoura, Morsi's opponents began pelting supporters with garbage as they gathered outside a mosque for a pro-regime march, al-Arabiya said.
Egyptian police failed to disperse the clashes despite the use of teargas and violence continued into the night, a Health Ministry source told Ahram Online. Shops and cars were damaged, al-Masry al-Youm, said.
Clashes were also reported in Alexandria.
Anti-Morsi activists plan a massive protest for Sunday to demand he step down, Ahram Online reported. Counter-rallies by the president's supporters were planned for Friday.
The Egyptian army has warned it will intervene to prevent chaos, al-Arabiya said.
Anti-Morsi activists said they collected 13 million signatures on a petition calling for him to step down and seeking early presidential elections to replace him, the BBC said. Morsi supporters counter that any move to unseat him now would be undemocratic.