The announcement, however, did not signal a resolution of the tensions between Morsi and the Egyptian judiciary, Ahram Online reported.
Presidential spokesman Yasser Ali said Morsi's decree last week excepting decisions from judicial review will not be modified, though he said it may have been "misunderstood" by the public.
"The decree will only immunize the president's sovereign decisions [from legal challenges]," Ali said in a statement after Morsi met with senior jurists.
Ali said the presidential action was temporary and stressed Morsi's respect for Egypt's judicial institutions and their independence.
Egyptian newspaper al-Masry al-Youm reported members of the Supreme Judicial Council indicated there was no resolution but declined to elaborate on where the matter stands.
"We have nothing more than what was included in the presidential statement," Judge Ahmed Abdel Rahman, deputy head of the Court of Cassation and member of the Supreme Judicial Council, told al-Masry al-Youm.
Exactly what Morsi means by "sovereign matters" was being parsed by analysts. Some said it implies the Constituent Assembly and Shura Council cannot be dissolved, while other presidential decisions could be challenged in court.
Morsi has called on judges to keep working to preserve citizens' rights, Ali said.
Ali said the president stressed that retrials of those accused of killing protesters during the uprising against President Hosni Mubarak would be conducted only if investigations reveal new evidence is presented.
The president's office has insisted Morsi was forced to invoke new powers, which set off violent protests, to protect the process of writing the country's new Constitution. It said the decree, issued Thursday, would be lifted once the charter is in place.
"The presidency reiterates the temporary nature of those measures, which are not intended to concentrate power, but to avoid ... attempts to undermine democratically elected bodies and preserve the impartiality of the judiciary," Morsi's office said.
Egyptian Justice Minister Ahmed Mekki, an independent Cabinet minister, had met with the jurists Sunday seeking to broker a deal, state television reported. After that meeting, the council urged Morsi to scale back his writ, The New York Times reported.
Mekki, a close Morsi aide, also went on television to urge Morsi to narrow the decree's scope so it would no longer place all the president's future edicts above judicial scrutiny -- the provision that provoked the greatest outcry.
He said the decree should be limited only to functions of the Constitution-writing Constituent Assembly and the upper house of Parliament.
"I believe it is the duty of the president" to limit the decree's scope, Mekki told state TV. As written, the decree "violates my core convictions," he said.
Many Egyptian courthouses were closed Sunday after the nation's judges went on strike, Egyptian state media said.
The Egyptian stock market's key stock index fell 9.6 percent Sunday, erasing more than $4 billion of value.
More than 1,000 activists clashed with riot police in and around Cairo's Tahrir Square, the epicenter of the uprising that toppled Mubarak in February 2011 and brought Morsi to power.
More than 500 people were reported injured.
Some rocks had landed in the U.S. Embassy compound near the square, the embassy said, adding it didn't think it was the target.
Still, it urged embassy personnel to remain indoors and warned U.S. citizens against going to the embassy.
A 15-year-old Muslim Brotherhood supporter was killed in a clash in a Brotherhood political Freedom & Justice Party office in Damanhour, 100 miles northwest of Cairo and 40 miles east-southeast of Alexandria in the western Nile Delta, the party said.
Scores of others were injured, security officials said.
The office was one of many party offices burned or looted Sunday, the party said.
Party spokesman Nader Omran told the Times he blamed the attacks on an organized conspiracy.
Opposition groups called for a million-strong gathering in Tahrir Square Tuesday.
The Brotherhood, which initially called for a similar rally Tuesday in nearby Abdeen Square, next to Morsi's principal workplace, changed the venue Sunday to a public space farther from the square to avoid clashes with Morsi opponents.