Police fired tear gas as scores of opponents of the constitution and thousands of Islamists hurled rocks across a security cordon separating them near a mosque in Alexandria that was the focus for violence last week.
"God is great," Islamists chanted when the clash began.
The Islamists had gathered in support of an Islamic vision of Egypt's future a day before a second round of voting in a referendum on the basic law. Opposition supporters had also turned out as worshippers assembled for Friday prayers.
Morsi and his Islamist allies back the draft constitution as a vital step in Egypt's transition to democracy almost two years after the fall of Hosni Mubarak.
The opposition says the draft, drawn up by an Islamist-dominated assembly, is a recipe for deepening divisions and more violence.
The Muslim Brotherhood called for the mass gathering in Alexandria to protest after a violent confrontation between Islamists and the liberal, secular opposition last week ended with a Muslim preacher besieged inside his mosque for 14 hours.
Rival factions had used clubs, knives and swords last week, but this time police kept the feuding sides apart, although witnesses saw several protesters and one police being helped away. Some protesters had head wounds.
The run-up to the final round of voting on a new constitution on Saturday has been marked by often violent protests that have cost at least eight lives. The first round on December 15 produced a "yes" vote that is expected to be repeated in the second round.
Lines of riot police cordoned off Alexandria's al-Qaid Ibrahim mosque, scene of last week's violence. Islamists chanted pro-Islamic slogans while a smaller group of opponents gathered nearby, chanting against Morsi, propelled to power in a June election by the Muslim Brotherhood.
"The people want the implementation of sharia," the Islamist sympathizers shouted, in a show of support for Islamic law. "Our souls and blood, we sacrifice to Islam," they shouted.
In one incident, an Islamist filming anti-Morsi protesters was grabbed and roughed up. Islamists on the other side of a security cordon pushed and shoved police trying to reach him.
The opposition, facing defeat in the referendum, has called for a "no" vote against a document it says is too Islamist and ignores the rights of women and minorities, including the 10 percent of Egyptians who are Christian.
Anti-Morsi protester Ali al-Banna, a 51-year-old businessman, said: "We reject the constitution. Morsi's legitimacy has collapsed and we will bring him down."
The first day of voting on December 15 resulted in a 57 percent majority in favour of the constitution. The second stage on Saturday is expected to produce another "yes" vote as it covers regions seen as more conservative and likely to back Morsi.
The National Salvation Front, the main opposition coalition, said a "no" vote meant taking a stand against attempts by the Brotherhood to dominate Egypt.
The constitution must be in place before a parliamentary election can be held. If it passes, the poll should be held within two months.
Demonstrations erupted when Morsi awarded himself sweeping powers on November 22 and then fast-tracked the constitution through a drafting assembly dominated by his Islamist allies and boycotted by many liberals.
The referendum is being held over two days because many of the judges needed to oversee polling stayed away in protest. In order to pass, the constitution must be approved by more than 50 per cent of those voting.
Adding to the uncertainty as the final round of the referendum approaches, Egypt's chief prosecutor suddenly announced that he was retracting his decision to quit.
Prosecutor Talaat Ibrahim had resigned after more than 1,000 members of his staff gathered at his office to demand he step down because his appointment by the president, rather than by judicial authorities, threatened the judiciary's independence.
Ibrahim said he changed his mind because he had quit under duress.