CAIRO — President Mohamed Morsi agreed Monday to scale back a sweeping decree he had issued last week that raised his edicts above any judicial review, according to a report by a television network allied with his party. The agreement, reached with top judicial authorities, would leave most of Morsi’s actions subject to review by the courts but preserve a crucial power: protecting the constitutional council from being dissolved by the courts before it finishes its work.

The Muslim Brotherhood, the Islamist group that sponsored Morsi and his party, announced that it was canceling a major demonstration in support of the president that had been planned for Tuesday.