At least 38 people, including civilians and soldiers, have been killed there in the past two days.

In a speech Sunday night, Morsy decried the behavior of "criminals," saying recent violence "does not have anything to do with the Egyptian revolution. ... In fact, it is against the revolution."

But he acknowledged the legitimate dissent in Egypt, saying "dialogue is the only way to bring about stability and security."

To this end, he invited representatives from 11 political parties to a meeting Monday.

But a key opposition leader issued conditions before accepting Morsy's call for dialogue.

"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.

On Sunday, the National Salvation Front called for "peaceful protests" and held the president responsible "for the excessive violence used by security forces against protesters," 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 Monday.

"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.