Lewis Hamilton says he "won't let up" in his fight against injustice as the FIA decided not to investigate his actions at the Tuscan Grand Prix.
Formula 1's governing body had been considering whether Hamilton broke its rules in wearing a T-shirt highlighting police brutality at Sunday's race.
An FIA spokesman told BBC Sport an investigation had been ruled out.
Hamilton said: "Want you to know I won't stop using this platform to shed light on what I believe is right."
The Mercedes driver, writing on Instagram, thanked "those of you who continue to support me and show love, I am so grateful".
He added: "This is a journey for all of us to come together and challenge the world on every level of injustice, not only racial."
Hamilton's T-shirt, which he wore for the pre-race anti-racism demonstration and on the podium afterwards, said: "Arrest the cops who killed Breonna Taylor" and "Say her name".
Taylor was a black woman who was shot eight times in her home in Louisville, Kentucky, by US police in March.
She was one of a number of victims of incidents involving police violence in the US whose names have become rallying cries for equality and justice.
The FIA was caught by surprise by Hamilton's actions - previously he had worn a T-shirt saying "Black Lives Matter", while those of all other drivers have said "End Racism".
It had been considering whether Hamilton had breached article 1.2 of the FIA statutes, which says: "The FIA shall refrain from manifesting discrimination on account of race, skin colour, gender, sexual orientation, ethnic or social origin, language, religion, philosophical or political opinion, family situation or disability in the course of its activities and from taking any action in this respect."
The FIA is also a signatory of the Olympic charter, which forbids any "kind of demonstration or political, religious or racial propaganda".
Hamilton said after winning the race on Sunday: "I've been wanting to bring awareness to the fact there are people being killed on the street.
"And someone was killed in her own house and they were in the wrong house and those guys are still walking free."
F1 and the FIA have mounted an anti-racism and pro-diversity campaign this year, which includes anti-racism demonstrations before every race.
Hamilton has been at the centre of the demonstrations, as the sport's most high-profile figure and its only black driver.
His stance has been backed by his Mercedes team, who painted their cars black this year to represent their support for anti-racism and diversity.
Mercedes F1 boss Toto Wolff said on Saturday that Hamilton had the organisation's full support in his desire to highlight racial injustice and that it was up to him what T-shirts he wished to wear to demonstrate that.
"No question - it is entirely his decision," Wolff said. "Whatever he does, we will support. The team is fighting against any kind of racism and discrimination and it is Lewis's personal fight for Black Lives Matter and with all the support we can give him. It's his call."
Wolff added: "Black Lives Matter is something that is important to all of us and we have supported Lewis all the way.
"The much broader movement is obviously the fight against any kind of racism and discrimination and we as a team and as a corporate have always put an emphasis to fight against that injustice."
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