England prop Joe Marler has been banned for two matches and fined £20,000 for calling Wales forward Samson Lee "Gypsy boy".
Marler, 25, had avoided punishment by Six Nations organisers, but World Rugby conducted its own investigation.
Six Nations Rugby said it "has no difficulty" with being overruled by the game's global governing body.
The Rugby Football Union said Marler would not appeal against the decision and considered the matter closed.
Marler made the comment in England's Six Nations win over Wales in March and had an apology accepted by Scarlets prop Lee, who is from the Traveller community.
World Rugby said it had "exercised its right to take appropriate action before an independent judicial committee in the absence of such a process by Six Nations Rugby in accordance with the regulations".
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In a statement, Six Nations Rugby said it had made it clear it did not condone what Marler had said but would not take any further disciplinary action against him.
"Six Nations Rugby fully co-operated with World Rugby's disciplinary process in this case, and fully supports and endorses World Rugby's disciplinary regime in international rugby," it added.
Harlequins forward Marler, whose fine will be donated to an equality charity in the UK, admitted to a misconduct charge at a disciplinary hearing in London on Tuesday.
He will miss his club's Challenge Cup quarter-final against London Irish on Saturday and next weekend's Premiership trip to leaders Saracens.
Marler was free to play in England's final game of the Six Nations - starting on the bench in a Grand Slam-clinching 31-21 victory over France in Paris - after competition organisers decided the incident did not require punishment.
The Welsh Rugby Union issued its own statement at the time, saying it was disappointed with the Six Nations' decision not to punish Marler.
England head coach Eddie Jones reprimanded Marler after the incident, but Lee, 23, dismissed it as "banter".
Wales head coach Warren Gatland also described the comment as "banter", but he later apologised for his remark.
Campaigners from the Traveller community - and figures inside the sport - had been critical of Marler for making the comment and called for a ban.
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