The secular, liberal and left-wing opposition denounced what it called a planned "Brotherhoodisation" of the judiciary and called for demonstrations outside parliament.
A presidential source said Mursi met the Supreme Judicial Council and the prosecutor general to discuss a draft law reforming the judiciary due to go through the Islamist-dominated upper house on Wednesday.
Justice Minister Ahmed Mekky tendered his resignation on Saturday following a protest by Mursi's Islamist backers to demand that judges appointed during ousted former President Hosni Mubarak's nearly 30-year rule be purged.
A key provision of the draft proposed by the Brotherhood's Freedom and Justice Party would lower the mandatory retirement age for judges to 60 from 70, forcing hundreds of members of the judiciary to step down immediately.
Critics say it would eliminate more than 3,000 judges at a stroke, including most members of senior bodies such as the constitutional court which has repeatedly stymied Mursi's legislative and election plans.
Leaders of the opposition National Salvation Front called for demonstrations outside the Shura Council (upper house) on Wednesday to protest against what one senior liberal politician, Mohamed ElBaradei, called "the judges' massacre".
"The true goal of this project is to 'Brotherhoodise' the judiciary and replace independent judges with Brotherhood elements," the umbrella group said in a statement.