But 23 people died, health officials said, and hundreds more were injured in clashes overnight at Cairo University, the state-funded Al-Ahram news agency reported.
Protest leaders have called for nonviolence.
Egypt's military met Wednesday with religious, national, political and youth leaders to address the crisis, Egyptian military spokesman Ahmed Ali said through his Facebook page.
Hours earlier, an opposition spokesman accused the United States of propping up Morsy out of concern for neighboring Israel.
"The hour of victory is coming," said Mahmoud Badr of the Tamarod opposition group. He predicted that the "illegitimate president" would be gone by the end of the day.
"Not America, not Morsy, not anyone can impose their will on the Egyptian people," Badr said.
With the ultimatum, the armed forces appeared to have thrown their weight behind those opposed to Morsy's Islamic government.
Early Wednesday, soldiers and police set up a perimeter around the opposition's central meeting point, Cairo's Tahrir Square, "to secure it from any possible attack," the state-run EgyNews agency reported.
It was the police who, on the same spot in 2011, killed hundreds when they fired upon democratic, moderate and Islamic demonstrators seeking to overthrow Hosni Mubarak, the country's longtime autocratic leader and U.S. ally.
Mubarak had long repressed the Muslim Brotherhood, an Islamic political movement that emerged as the nation's most powerful political force once Mubarak was ousted.
Many of the democratic reformers and moderates who accused Morsy's government of moving in an authoritarian direction now support former Mubarak allies and others fed up with the nation's direction in calling for the restoration of order through the military.
They are pushing to oust Morsy and his Muslim conservative government, whose leaders were drawn primarily from the ranks of the Muslim Brotherhood. They say they have collected more than 20 million signatures on a petition to remove him -- millions more than the number who voted Morsy into the presidency.
In recent days, anti-Morsy demonstrators have ransacked Muslim Brotherhood offices all over the country.
Brotherhood members have complained that police did not protect them. Some have taken matters into their own hands, in one instance firing upon vandals with shotguns, an international journalism association reported.
The military's plans
Military leaders have told Arab media that they plan to suspend the constitution, dissolve the parliament and sideline Morsy.
In his place, they would install a mainly civilian interim council until a new constitution can be drafted and a new president elected.
The military's ultimatum was intended to push all factions toward a national consensus, not to seize power through a coup, a spokesman, Col. Ahmed Ali, said Monday in a written statement.
The military appears to be pressuring Morsy to restructure his government to reduce the influence of the Muslim Brotherhood and include opposition members, a source close to highly placed members of Egypt's leadership told CNN.
That restructuring was already happening. Five of Morsy's ministers resigned this week, including Foreign Minister Mohamed Kamel Amr.
And former Prosecutor General Abdel-Meguid Mahmoud will meet Thursday with the Supreme Judicial Council to be officially confirmed in the job.
Mahmoud had originally been installed in the job by Mubarak, shortly before he left. One of the goals during the 2011 revolution had been to oust him, which Morsy did through last November's constitutional declarations.
Mahmoud's return appeared to signify a shrinking of Morsy's power and a tilt toward Mubarak-era officials over Muslim Brotherhood loyalists.
In addition, 30 members of the Shura Council, the upper house of parliament, have resigned, state-run Nile TV reported.