Prince Mohammed bin Nayef, who chairs the Saudi haj committee, ordered the probe during a meeting with senior officials responsible for the pilgrimage in Mina, where the stampede took place.
The findings of the investigation will be submitted to King Salman, “who will take appropriate measures” in response, the agency added.
Thursday’s tragedy comes on the heels of another one, in which 108 people were killed when a massive construction crane collapsed on Mecca’s Grand Mosque on Sept 11 as thousands were gathering for the haj.
At the time, Nayef said the accident would not affect this year’s pilgrimage and that the safety of pilgrims was a “priority”.
Earlier Thursday, Health Minister Khaled al-Faleh promised that there would be a rapid and transparent investigation of the stampede, which he blamed on undisciplined pilgrims not following instructions.