CAIRO — Egypt’s chief prosecutor ordered an investigation on Thursday into allegations that opposition leaders committed treason by inciting supporters to overthrow President Mohammed Morsi.

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 aconstitution that was drafted by Islamists and 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.