Sebastian Vettel has escaped punishment for his expletive-laden outburst at the Mexican Grand Prix in which he told race director Charlie Whiting to "f*** off".

Vettel, the four-time champion, swore repeatedly at Whiting and Max Verstappen over the team radio as he dramatically lost his cool when he clashed with the Dutchman in the closing stages of Sunday's race.

But following a letter of apology to FIA president Jean Todt and Whiting, the sport's governing body confirmed on Tuesday night that the German will face no further action.

The FIA said in a statement: "At the recent Mexican Grand Prix, the Ferrari driver Sebastian Vettel made comments over team radio using repeated foul language directed at both the FIA Formula 1 Race Director Charlie Whiting and a fellow competitor which were retransmitted during the live broadcast of the event.

"Immediately following this incident, Sebastian Vettel spontaneously sought out Charlie Whiting to express his regrets for his behaviour in person.

"He then, again on his own initiative, sent letters to each of the FIA President Jean Todt and Charlie Whiting, in which he apologised profusely for his actions. He also indicated that he would likewise be contacting Max Verstappen and vowed that such an incident would never occur again.

"In the light of this sincere apology and strong commitment, the FIA President has decided, on an exceptional basis, not to take disciplinary action against Mr Vettel by bringing this matter before the FIA International Tribunal."

Vettel in action at the Mexican Grand Prix (Getty)

Vettel's outbursts, which were transmitted during Sunday's race, overshadowed Lewis Hamilton's victory in Mexico.

The Ferrari driver was warned that he will face disciplinary action for a repeat offence.

"The FIA will always condemn the use of offensive language in motor sport - especially when directed at officials and/or fellow participants - and expects all participants in its Championships to be respectful and mindful of the example they set for the public and the younger generation in particular," the statement continued.

"The FIA takes this opportunity to advise that, in the event of any future incident similar to the one that occurred in Mexico, disciplinary action will be taken by bringing such incident before the FIA International Tribunal to be judged."