But it was not immediately clear whether his concession would satisfy an increasingly fierce opposition.
The Islamist leader annulled a controversial decree issued last month that put his decisions beyond judicial review -- a move denounced as a dictatorial "power grab" by the opposition, but one Morsi had defended as necessary to protect reforms.
"The constitutional decree is annulled from this moment," Selim al-Awa, an Islamist politician and advisor to Morsi told a news conference after a meeting between the president and other political leaders.
But Awa said that an equally contentious referendum on a new constitution would go ahead as planned on December 15.
The president was legally bound under the constitution to maintain that date and had no choice, he explained.
Awa added, though, that, if the draft constitution were rejected, a new one would be drawn up by officials elected by the people, rather than ones chosen by parliament as for the current text.
The draft constitution has been criticised for its potential to weaken human rights and the rights of women, and out of fear it would usher in Islamic interpretation of laws.
The two issues -- the decree and the referendum -- were at the heart of the anti-Morsi protests that turned violent this week with clashes on Wednesday that killed seven people and wounded hundreds.
The opposition refused Morsi's offer for dialogue as long as those two decisions stood.
But on Saturday, the powerful military, in its first statement since the crisis began, told both sides to talk, warning that otherwise Egypt would descend "into a dark tunnel with disastrous results -- and that is something we will not allow."
It underlined that it "stands always with the great Egyptian people and insists on its unity," but also said it was its duty to protect state institutions.
It urged a solution based on "democratic rules."
Morsi's concession on the decree appeared to be a gesture to open the way for the talks to happen. But it remained to be seen if the opposition would remain intransigent over the referendum.
On Saturday there were none of the large-scale demonstrations that had taken place on previous nights.
But the presidential palace remained ringed by tanks and troops, as it has been since the day after the deadly clashes.
In Cairo's Tahrir Square, a focal point for hardcore protesters, news of the annulled decree sparked no festivities or exuberance.
"This will change nothing," said one anti-Morsi activist, Mohamed Shakir, 50.
"Even if they offered us honey, it would not be enough," agreed another, Hisham Ezzat.
Ahmad Abdallah, there with his wife and two children, said he could no longer accept Morsi and nothing less than the disappearance of the Muslim Brotherhood backing the president would please him.
"The Brotherhood exists around the world, they have gone to other countries and split the people. Before the split, Morsi had a chance, but now it's too late," he said.
The main opposition bloc, the National Salvation Front, has said it is ready for "serious and objective dialogue" as soon as Morsi met its demands to scrap both the decree and the referendum.
It had rebuffed an earlier offer by Morsi on Thursday to open talks because the president did not give way on those two points.
In recent days, the mass protests had taken to demanding Morsi step down, in scenes reminiscent of those during the early 2011 uprising that toppled former president Hosni Mubarak from power.
Wayne White, a former senior US State Department intelligence official who is now a policy expert with Washington's Middle East Policy Council, told AFP that the military's involvement in the crisis was key.
If the army's leaders saw sufficient opposition to Morsi, they would "inform him that they cannot continue to keep the peace and that he should make serious concessions to the opposition," he said.