Stefano Domenicali says FIA president Mohammed Ben Sulayem is best to leave "everyday life" in Formula 1 to others.
Amid a particularly tense moment between the sport's governing body and the commercial rights holders at Liberty Media, Ben Sulayem told the teams last week that he will take a step back from the limelight.
One of the big controversies was the Ben Sulayem-promoted clampdown on the drivers' freedom to make political statements.
"I grew up in a country where we are all free to express our views and religions," Kevin Magnussen, from Denmark, said as he took the wheel for the Silverstone 'shakedown' of Haas' 2023 car.
"I think that's a value that I appreciate and would like to see in F1 as well."
Although Ben Sulayem is taking a step back, it is understood he will definitely be in Bahrain for the season opener next month.
But F1 CEO Domenicali insisted at the weekend that he believes the recent controversies are now largely in the past.
"The key to success is that everyone does their job in the best way," he is quoted by Sky Italia. "From us to the teams and drivers but also the FIA.
"As president, Mohammed should take care of strategic things and leave everyday life to others like us," added Domenicali, who heads F1 on behalf of Liberty Media.
"I hope to continue the discussions with him for the important decisions that affect our sport."
As for the 'free speech' ban, Domenicali says the FIA and F1 are now on a path to clarity.
"I think it's more a question of respect than of procedures," said the Italian. "I don't think anything will change from how we have done it in recent years.
"Nobody wants to put a gag on the drivers. I hope the FIA will share my vision," Domenicali added.
Domenicali is also quoted by De Telegraaf newspaper: "I do not believe the new rules are intended to prevent a driver from communicating with the community.
"I don't want a driver saying something to attack someone else - that's wrong. He also has to consider the sponsors.
"But if a driver draws attention to topics that are at the centre of social discussion, that is no problem and I think the FIA feels the same way."
