Hoyal said that Babbitt was skiing with three others when he fell. Two of his companions went down after him, while another stayed above the cliff to call for help. The man was conscious when rescuers located him.
Babbitt told rescue workers he did not intend to go over the cliff, but it's not clear whether he was skiing out of control, or simply got too close to the edge and was unable to prevent himself from going over, Hoyal said.
"He did tell us it was accidental," Hoyal said.
Snowbird spokeswoman Emily Moench said the fall occurred in the Pfeifferhorn peak area, which is west of Snowbird and far outside of the resort's boundaries. But Moench confirmed that two Snowbird ski patrol members assisted in the search and rescue.
One of the tallest in the Wasatch Mountains, the Pfeifferhorn stands more than 11,300 feet above sea level.
Babbitt was listed in critical condition on Monday night, Hoyal said.