"Three people were killed and seven others wounded by birdshot and stabbing attacks during clashes between Morsi supporters and his opponents," Adel Said, a hospital official in the Nile Delta city of Mansura, told AFP.
The three killed Friday were all women, he added.
A pro-Morsi protester injured in the clashes, also speaking by phone, said thousands of loyalists were marching through the city's narrow streets when "thugs" attacked them with guns, knives and rocks.
Tensions are running high in Egypt more than two weeks after the army ousted the country's first freely-elected president following massive protests calling for him to go.
Rival protests were staged in several cities on Friday, with tens of thousands rallying in Cairo to demand the Islamist leader's reinstatement.
Before Friday's demonstrations, the army warned that it would decisively confront any violent protesters.
"Whoever resorts to violence in Friday's protests will endanger his life, and will be treated with utmost decisiveness, within legal bounds," it said.
Morsi's army-installed successor Adly Mansour vowed to fight for stability against opponents he accused of wanting to plunge the crisis-hit country "into the unknown".
"We will fight the battle for security to the end. We will preserve the revolution," he said in a speech broadcast by state television on Thursday.
Several thousand supporters of Morsi's overthrow by the military descended on Cairo's Tahrir Square on Friday evening, setting off fireworks and chanting pro-army slogans.
Earlier, a vast crowd gathered at the Rabaa al-Adawiya mosque in the capital, where Morsi loyalists have camped out since the military overthrew him on July 3.
About 10,000 protesters then set off in the direction of an elite military compound, the scene of the deadliest violence since Morsi's overthrow, carrying pictures of the deposed president and chanting slogans.
But they were blocked by soldiers and armored vehicles.
Smaller rallies took place elsewhere in Cairo and Egypt's second city Alexandria after the Muslim Brotherhood had called for a day of protests dubbed "Breaking the Coup".
Morsi has been held in custody since his ouster and other senior Brotherhood leaders have also been detained, prompting international concerns.
UN rights chief Navi Pillay summoned the Egyptian ambassador in Geneva and requested information about those arrested in connection with the events of July 3, her spokesman said on Friday.
On the eve of the demonstrations, Mansour pledged to rein in those who wanted to push Egypt "into the unknown".
"We will fight the battle for security to the end. We will preserve the revolution," he said, in comments echoed by the army.
Although mostly peaceful, the pro-Morsi protests have resulted in deadly clashes, with the unrest claiming more than 100 lives in all, according to an AFP tally.
In the worst bloodshed, at least 53 people, mostly Morsi supporters, were killed outside the Cairo headquarters of the Republican Guard on July 8.
The Brotherhood accuses the army of committing a "massacre," while the military says it was responding to a "terrorist" attack.
The demonstrations by those celebrating Morsi's ouster have been far smaller since the mass rallies that swept the country in the days leading up to the coup.
In his speech, Mansour offered an olive branch to the Brotherhood, saying: "The framework of justice and reconciliation extends to all."
The movement has categorically refused to recognize Mansour's caretaker government, which was sworn in this week but with Islamist parties and movements totally absent.
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