The probe by a Morsi-appointed prosecutor was launched a day after the president called for a dialogue with the opposition to heal rifts opened in the bitter fight over an Islamist-drafted constitution just approved in a referendum.
The opposition decried the investigation as a throwback to Hosni Mubarak’s regime, when the law was used to smear and silence opponents.
The probe is almost certain to sour the already tense political atmosphere in the country.
The allegations initially were made in a complaint by at least two lawyers sent to the chief prosecutor earlier this month. They targeted opposition leaders Mohamed ElBaradei, a Nobel Peace laureate and former head of the U.N. nuclear agency; former Foreign Minister Amr Moussa; and Hamdeen Sabahi.
Mr. Moussa and Mr. Sabahi were presidential candidates who competed against Mr. Morsi in the last election.
There was no immediate comment by any of the three opposition leaders named, but the opposition dismissed the allegations.
Emad Abu Ghazi, secretary-general of the opposition party Mr. ElBaradei heads, said the investigation is “an indication of a tendency toward a police state and the attempt to eliminate political opponents.” He said the ousted Mubarak regime dealt with the opposition in the same way.
Mubarak jailed his opponents, including liberals and Islamists. International rights groups said their trials did not meet basic standards of fairness.
Mr. ElBaradei was a leading figure behind the uprising against Mubarak, and at one point, he was allied with the Brotherhood against the old regime.
The investigation does not necessarily mean charges will be filed against the leaders. But it is unusual for state prosecutors to investigate such broad charges against high-profile figures.
Mr. Morsi, Egypt’s first democratically elected president, asked the opposition Wednesday to join a national dialogue to heal rifts and move on after a month of huge street protests against him and the constitution drafted by his allies.
Some of the protests erupted into deadly violence. On Dec. 5, anti-Morsi demonstrators staging a sit-in outside the presidential palace in Cairo were attacked by Morsi supporters. Fierce clashes ensued that left 10 people dead.
The wave of protests began after Mr. Morsi’s Nov. 22 decrees that gave him and the assembly writing the constitution immunity from judicial oversight. That allowed his Islamist allies on the assembly to hurriedly rush through the charter before an expected court ruling dissolving the panel.
After the decrees, the opposition accused Mr. Morsi of amassing too much power in his hands. They said the constitution was drafted without the participation of liberal, minority Christian and women members of the assembly, who walked out in protest at the last minute.
Even though the constitution passed in a referendum, the opposition has vowed to keep fighting it. They say it enshrines Islamic law in Egypt, undermines rights of minorities and women, and restricts freedoms.
Mr. Morsi and Brotherhood officials accused the opposition of working to undermine the president’s legitimacy, and accused former regime officials of working to topple him.
Although he reached out to the opposition for reconciliation, Mr. Morsi did not offer any concessions in his speech Wednesday calling for a dialogue.