To this end, he invited representatives from 11 political parties to a meeting.
But a key opposition leader issued conditions before accepting Morsy's call for talks.
"Without accepting his responsibility as a president for the latest bloody events, promising to form a government of national salvation and commissioning a balanced committee to amend the constitution, any dialogue will be a waste of time," said Mohamed ElBaradei, head of the Constitution Party and a member of the opposition National Salvation Front.
Protests could drag on
The National Salvation Front held the president responsible "for the excessive violence used by security forces against protesters" and called for peaceful demonstrations, according to a statement posted on the state-run Al-Ahram news website.
The group made several demands before it would urge people to stop protesting, including the formation of a new government and making changes to what it called the "distorted constitution" that voters passed in a referendum last month.
Morsy's supporters warned the opposition against such demands.
"We would like for the political forces, especially the National Salvation Front, to realize how important this defining moment is and to put the interest of the nation above all," said Gamal Tag, senior leader of the Freedom and Justice Party, the political wing of the Muslim Brotherhood.
"They need to know that President Morsy's call for dialogue is not out of weakness, but it is out of his responsibility as president. ... Some forces are still putting conditions and obstacles before this national dialogue in order to make it fail. These people do not put forward the national interest. They are looking for personal gains."
U.N. human rights official weighs in
The scores of deaths prompted Navi Pillay, the U.N. high commissioner for human rights, to denounce the violence and call for dialogue among all parties.
"While at least two policemen are among those killed, preliminary unconfirmed reports suggest that most of the casualties have been caused by live fire and excessive use of tear gas by the authorities," a statement from Pillay's office said.
In addition, as many as 25 female protesters reportedly have been sexually assaulted in Cairo's Tahrir Square over the past few days, "in some cases with extraordinary violence," the statement said.
She said the state of emergency should be governed by the rule of law, in line with international standards. She urged Morsy to listen to the demands of demonstrators and take action to deal with problems in the judicial system. She said that all "stakeholders" should be involved in reviewing legislation on demonstrations, associations and access to public information.
"I urge the government to take urgent measures to ensure that law enforcement personnel never again use disproportionate or excessive force against protesters, firstly because it is illegal to do so, and secondly because it is likely to make the situation even more explosive," Pillay said.