Lewis Hamilton and Romain Grosjean they had cleared the air after the six-times Formula One champion accused the Haas driver of wanting to drop anti-racism protests.
Mercedes driver Hamilton had spoken critically of Grosjean, a director of the Grand Prix Drivers' Association (GPDA), following a rushed and disorganised gesture before the Hungarian Grand Prix on July 19.
"He doesn't think it's important to do it. He's one of them that thinks that it was done once and that's all we need to do," the Briton, Formula One's only Black driver and prominent among those taking a knee, said at the time.
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Grosjean told reporters at the British Grand Prix that he had a 45-minute phone conversation with Hamilton on the Tuesday after the race.
"I said to Lewis 'Look, maybe I did it wrong'," he said.
"I felt that as one of the directors, (co-director) Sebastian (Vettel) was pushing in the direction of carrying on "End Racism", which is the right approach, I was speaking for the drivers that were not happy to carry on, to express their voice.
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"Thinking about it, it was probably the wrong thing to do, Lewis had some good arguments, I had some also, but I think it was the wrong thing to do."
Grosjean said the GPDA had spoken with F1 chairman Chase Carey and Jean Todt on a conference call to make sure things were done in the right way in future with a clear procedure before the race.
"I think that's going to happen," he said.
Hamilton, speaking separately, said he had been impressed by his conversation with Grosjean and appreciated the Frenchman's approach.
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"He originally reached out to me to talk after the last race, and we had this great conversation," he said.
"The fact is, we have more in common than we perhaps think. He's clearly a caring person.
"It's not easy for anybody to admit that we're wrong...when we got off the phone I knew that we were united and we're going to be working towards the same common goal," he added.