CAIRO — Egypt’s Islamist president proclaimed the country’s newly adopted constitution as the dawning of a ‘‘new republic’’ in a television address Wednesday, calling on the ­opposition to join a dialogue with him after a month of violent turmoil and focus on repairing a damaged economy.

Mohammed Morsi sought to present the Islamist-drafted charter as the turning of a historic page for Egypt, but his speech did little to ease the suspicions of those who fear he and his Muslim Brotherhood are entrenching their power. He offered no concrete gestures to an opposition that has so far rejected his dialogue and vowed to fight the constitution.