Egyptian President Mohammed Morsy said he will not step down and vowed to protect “constitutional legitimacy” with his life, as millions took to the streets nationwide demanding his ouster.

“My life is the price for protecting the legitimacy,” he said in a televised speech late Tuesday. “If my blood was the price to maintain legitimacy, then I am ready for this for the sake of this nation’s stability.” The national address came as an ultimatum by the Egyptian Army -- for Mr. Morsy and rival factions to reach consensus or see military intervention to end the political stalemate -- was due to expire Wednesday.

“The people chose me,” the Islamist president said. “The people designated me through free, clean elections.” Egypt’s first democratically elected president, Mr. Morsy blamed members of the former regime of ousted president Hosni Mubarak for inciting protests against him and violence in the streets.

Mr. Morsy admitted shortcomings in his rule but said “corruption and remnants of the old regime” were hindering progress. His offer for dialogue with the opposition continues, said Mr. Morsy, who promised a series of measures including replacing the cabinet and holding parliamentary elections.

After his 45-minute speech, opponents in central Cairo’s Tahrir Square chanted “Leave!” The opposition demand Mr. Morsy’s ouster and called for early presidential elections and drafting of a new constitution.

Clashes erupted early on Wednesday in another pro-government rally near Cairo University. State television reported several people killed and injured.

Gun battles and street fighting left at least two people dead Tuesday as Mr. Morsy’s supporters and opponents exchanged fire and clashed with knives and sticks in at least three areas of Giza province on the outskirts of Cairo.

Thirty-three people were injured in the northern city of Alexandria in clashes with guns loaded with birdshot, health official Amr Nasr said.

The southern city of Luxor saw clashes with guns and rocks as Egyptians rallied nationwide after rival political groups called for followers to take to the streets as the army’s deadline approached.

Mr. Morsy-allied Islamists insisted they did not initiate the fighting.

“We will not resort to violence, but with peaceful methods we will stand by Mr. Morsy to our last breath,” Ali Rifaei said as he joined a pro-government rally near Cairo University.

They have vowed that Mr. Morsy would complete his four-year term, which ends in 2016.

“Are you trying to tell me that my vote is worth nothing?” asked Ihab Rafi, a 43-year-old finance manager. “This is the core of the problem. We are not sheep. We are people.” Mr. Morsy’s opponents gathered in Tahrir Square and near two presidential palaces in Cairo.

The largely secular opposition accuses Mr. Morsy of serving the interests of his Muslim Brotherhood group and failing to revive the economy.

The military said Monday that it would announce measures by Wednesday to end the political stalemate.

The opposition took the ultimatum to mean Mr. Morsy would be ousted, and Mr. Morsy’s supporters called it a coup. The military denied such an interpretation and said it was aimed at pushing all political factions to reach a consensus.

In what appeared as an attempt to appease anti-Morsy protesters, the army released footage taken by military helicopters of the masses that rallied against Mr. Morsy on Sunday, his first anniversary in office.

Troops were shown training in the streets of the Red Sea city of Suez, according to footage on Al-Jazeera’s Egyptian arm, Al-Jazeera Masr.

Military helicopters flew over anti-Morsy rallies in Cairo for the third consecutive day.

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