Ecclestone, however, wants Mosley to go later this year, in November, rather than risk being forced to quit in a show of no-confidence on Tuesday.
"I don't want to see that. I've been a friend of Max for 40 years. I would hate to see him go in this way after all he has done for the sport," he said.
Ecclestone said the fallout of the sex scandal, triggered when News of the World caught Mosley in a sadomasochistic romp with five prostitutes, had left him under "enormous pressure" from the sport's stakeholders.
"He should stand down out of responsibility for the institution he represents, including F1. Everyone who I speak to in a position of authority across F1 rings me to say he should leave.
"It is regretful that he has not made that decision," Ecclestone added.