During a phone call with Morsi, Obama expressed "deep concern about the deaths and injuries of protesters in Egypt," the White House said in a statement.
"The president emphasized that all political leaders in Egypt should make clear to their supporters that violence is unacceptable," the statement said. "He welcomed President Morsi's call for a dialogue with the opposition but stressed that such a dialogue should occur without preconditions."
Obama noted the United States has urged Morsi's opponents to engage in such dialogue as well.
Morsi said Thursday he respects peaceful opposition but protesters who resort to violence "will not escape punishment."
Morsi spoke on television at the end of a day on which more government officials resigned amid violence in Cairo in which at least six people died in clashes with military forces at the presidential palace.
Morsi addressed his comments to supporters and opponents alike, condemning in particular those who have used weapons against protesters -- and who are supported by members of the "corrupt ... ex-regime" of former President Hosni Mubarak, CNN reported.
They "will not escape punishment," he said.
With Egypt facing its most serious conflict since the ouster of Mubarak, a tense calm prevailed in Cairo's streets Thursday after a night of violence between Morsi opponents and supporters.
An estimated 450 people have been injured in the clashes, The New York Times reported. The Interior Ministry said about 3,000 security personnel were deployed around the presidential palace late Wednesday and some fired tear gas at protesters to disperse them, the privately owned Egypt Independent said.
Nine Morsi government officials, including Zaghoul el-Balshi, who headed the commission overseeing a Dec. 15 referendum on a proposed new constitution, have resigned, blaming Morsi for the bloodshed.
The director of state broadcasting resigned Thursday, along with Rafik Habib, vice president of the Muslim Brotherhood's Freedom and Justice Party. Habib, a Christian, had been held up as evidence of the Muslim Brotherhood's tolerance and diversity, the Times said.
Balshi was among those who resigned late Wednesday.
"I will not participate in a referendum that spilled Egyptian blood," he said.
Egyptian Prime Minister Hesham Qandil implored both sides in a statement to pull back to allow for "a national dialogue."
The fighting outside the presidential palace injured more than 350 people, the Health Ministry said, as Islamist supporters of Morsi, a former Muslim Brotherhood leader, fought secular opponents after the Islamists moved to break up an anti-Morsi demonstration Wednesday night, The Wall Street Journal reported.
The anti-Morsi camp complained the president had elevated himself to a dictatorial level when he seized sweeping powers Nov. 22 to legislate without the oversight of any court, removing the last check on his authority. He said he would give up the powers after ratification of the new constitution.
Demonstrators threw rocks and Molotov cocktails and brawled in the streets of affluent Cairo neighborhoods, news organizations reported.
Around midnight, police formed a barrier between the battling camps, with thousands of demonstrators on each side. Gunshots rang out and each side accused the other of firing live rounds.
Police fired tear gas into the crowd divided by the cordon.
As fires burned in the streets, clashed persisted and hundreds of pro-Morsi demonstrators spread blankets on the pavement in front of the palace to hold their territory, the Journal said. Members of the pro-Morsi crowd pummeled and dragged a man they characterized as an opposition thug, the newspaper said.
At least 32 people were arrested, the Interior Ministry said.
Protests were also ignited in other cities and Muslim Brotherhood offices were set on fire in Ismailia, 80 miles northeast of Cairo on the Suez Canal, and Suez, 90 miles east of Cairo on the Gulf of Suez.