Egyptian President Mohammed Mursi says the decree giving him sweeping new powers is temporary and not intended to concentrate power in his hands.
A statement from his office said Mr Mursi was committed to finding "common ground" with other parties. He will meet senior judges on Monday.
The decree was intended to prevent democratically elected bodies from being undermined, the statement said.
A youth was killed on Sunday - the first death since the protests began.
Described as a member of the Muslim Brotherhood, the movement that backs Mr Mursi, 15-year-old Islam Fathy Massoud was killed in the Nile Delta town of Damanhour after its headquarters were attacked. Sixty others were injured.
Clashes continued on Sunday, with police firing tear gas in Cairo's Tahrir Square area.
Large demonstrations are planned by supporters and opponents of Mr Mursi on Tuesday.
On Saturday the Judges Club, which represents judges throughout the country, called for a nationwide strike in protest at the decree.
But top judicial body the Supreme Judicial Council appeared not to reject the decree outright, saying it should only apply to "sovereign matters", and urged judges to return to work.
Justice Minister Ahmed Mekky has begun efforts to mediate between the president and the judges.
The minister said he himself had some reservations about the president's decree, Reuters reported.
'Committed to engage'
The BBC's Jon Leyne in Cairo says Mr Mursi has begun efforts to reach a compromise after the strong opposition to his decree.
A statement by the presidency attempted to calm opposition concerns that he was becoming increasingly dictatorial in his leadership.
"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," the statement said.
Mr Mursi said he was committed to dialogue.
"The presidency stresses its firm commitment to engage all political forces in the inclusive democratic dialogue to reach a common ground and bridge the gap in order to reach a national consensus on the constitution which will be the cornerstone of Egyptian modern institutions," the statement added.
Later local media reported that the president would meet the Supreme Judicial Council on Monday to discuss the decree.
But several prominent opposition leaders, including Nobel Peace Prize winner Mohamed elBaradei, have said they will not engage in dialogue with the president until he rescinds the measure, known as the constitutional declaration.
According to President Mursi's decree, no authority can revoke presidential decisions.
There is also a bar on judges dissolving the assembly, which is drawing up a new constitution.
Mr Mursi sacked chief prosecutor Abdel Maguid Mahmoud, who was first appointed by ex-President Hosni Mubarak.
Mr Mahmoud's replacement, Talaat Ibrahim, has been given the job of re-examining all investigations into the deaths of protesters when Mr Mubarak was in power.