Last month the former Formula One chief called Putin a "first-class person," adding he'd "take a bullet" for him.
The British business magnate, who has repeatedly gotten himself into hot water for his comments, said Russia's president is a "first-class" person.
The sport is set to undergo some "aggressive" changes.
Carey wants to add to the United States Grand Prix.
Liberty Media completed its F1 takeover in January.
Hamilton is aiming for a fourth world title.
Mosley told Newsweek he would not have removed Ecclestone as Formula One CEO.
Formula One enters a new era in 2017.
Ecclestone has been involved with the sport since the late 1950s.