F1 staged an organised pre-race kneel ahead of the opening race of the 2020 season in Austria last month in a strong anti-racism message.
The drivers organised the gesture themselves ahead of the next two races and had less time to make arrangements, leading to a fractured and messy display that drew criticism from many members of the grid.
Six-time world champion Lewis Hamilton said it felt like the anti-racism messaging had "gone off the agenda" and was "lacking leadership" from F1's senior management.
"There needs to be leadership from the top," Hamilton said. "You need to come out with 'OK hey, this is what we want to do guys, and we want you all to be a part of it'.
"That should be announced or discussed from the top down. That should be coming from the higher powers that control and pull all the strings."
Hamilton said he would speak to FIA president Jean Todt and F1 CEO Chase Carey ahead of the British Grand Prix about the matter.
The FIA has now given drivers an additional 10 minutes in the pre-race schedule to ease some of the time constraints, and issued guidelines to drivers on what gestures they may want to consider ahead of the race.
Fourteen drivers have regularly knelt before the national anthem, with six opting to stand instead.
Speaking to select media including Motorsport.com ahead of Sunday's British Grand Prix, FIA president Todt said he had held "very constructive" talks with Hamilton on the matter.
Todt said the new guidelines were intended to "address the situation in a more structured way", conceding the gestures at the second and third races of the season "not as settled as they should have been."
But Todt said the FIA could not force drivers into activism or gestures they felt uncomfortable with, believing it was important to respect their personal views.
"Of course, we are happy to put a special attention to the end of racism topic, which will be done as long as people feel they want to do it," Todt said.
"I feel it would be completely inappropriate to push people to do something they don't feel. I feel we must respect. We have people, they go to church, they go to the temple, they go to synagogue. We must respect that."
Asked if by "people" he meant "drivers", Todt replied: "People, whoever. I want to respect each believer. And for me, what does matter, life does matter.
"My wife is Chinese. I think she deserves the same attention as white, black, everybody needs attention. Colour, religion, we need everybody. Life matters."
Hamilton has been the leading figure in F1's anti-racism messaging in recent months, and has established his own commission aimed at improving diversity within the sport.
Asked by Motorsport.com for his thoughts on Hamilton's leadership, Todt spoke of his admiration for the Mercedes driver.
"I do respect somebody who has beliefs, and tries to use his image, his voice, his leadership to protect something," Todt said.
"There are many things unfortunately we want to improve. I'm very much involved as FIA president and as the UN's Special Envoy for Road Safety about the victims on the roads.
"I do admire people who do engage for something where they feel they can bring something. Clearly if he can bring something to that.
"I admire that, and as much as we will be able to contribute, we will do it."