Qatar was one of the main supporters of Mursi and his Muslim Brotherhood during their year in power. Ties between Egypt and Qatar have been strained since then-army chief Abdel Fattah al-Sisi ousted Mursi in July 2013 after protests against his rule.
Cairo has accused Al Jazeera of being a mouthpiece for the now-banned Brotherhood - which it denies - and security forces closed its offices in the Egyptian capital hours after Mursi's ouster.
The decision to end those broadcasts follows a meeting on Saturday between Sisi, who has since won a presidential election, and a special envoy of the emir of Qatar. The meeting was the latest step in a Saudi-brokered effort to repair relations.
Saudi King Abdullah last month called on Egypt to back a deal under which Saudi Arabia, the United Arab Emirates and Bahrain agreed to end an eight-month diplomatic dispute over Qatar's support for the Brotherhood and promotion of "Arab Spring" revolts.
Sisi has also suggested that he is considering pardoning three Al Jazeera journalists currently jailed on charges of aiding a "terrorist organisation" by spreading lies.
Qatar is seen to have been supportive of the Brotherhood in Egypt, the UAE, and more recently Libya. It had given sanctuary to some Brotherhood members but in September asked seven senior figures from the group to leave, following months of pressure from its neighbours.
Al Jazeera said it was rolling AJMM into a new channel reporting live events from around the world, not just Egypt.
"AJMM has meanwhile temporarily ceased broadcasting until such time as necessary permits are issued for its return to Cairo in coordination with the Egyptian authorities," it said in a statement.