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The FSS published a statement by the Manchester United defender, who said media and fan criticism over his recent performances for Serbia had persuaded him to hang up his international boots.
"The basic reason for my international retirement is that my commitment for the national team has been criticised by the media and therefore by the public as well for some time now," the FSS website quoted Vidic as saying.
"I've been under fire although I turned up to play for Serbia even when I was injured and sometimes I did so against the advice of my club."
His international retirement follows that of fellow top Serbian player Dejan Stankovic but Vidic hopes the team can now thrive.
"I have come forward with this statement in order to root out any hear-say talk as to why I'm quitting the national team, to make sure they keep a good atmosphere ahead of the 2014 World Cup qualifiers," added the centre back.
"I am also convinced the upcoming generation has the potential to give the nation plenty to cheer about and I will be with them whole-heartedly as a fan."
MISSED PENALTY
Vidic, who has scored two goals in 56 internationals, could not have ended his Serbia career on a more sour note after missing a penalty in a 1-0 defeat by Slovenia on October 11 which knocked Serbia out of contention for next year's finals.
Having won the man of the match award on his debut, a 1-1 Euro 2004 qualifying draw against Italy in October 2002, Vidic quickly became the backbone of the national team's defence.
However, he missed all three games in the 2006 World Cup when Serbia and Montenegro played as one country and lost all their matches.
Vidic, who had joined Manchester United from Spartak Moscow in January that year, was suspended for Serbia and Montenegro's opening 1-0 defeat by Netherlands and injured his knee in practice ahead of the 6-0 drubbing by Argentina.
He was flown home to Belgrade, where he had won one league title with 1991 European Cup winners Red Star, before the final 3-2 defeat by Ivory Coast.
Vidic first came under fire after giving away a needless penalty in Serbia's 1-0 win over Germany in the 2010 World Cup and was then blamed for a crunch 2-1 defeat by Australia which knocked the Serbs out of the competition.
Australia's opening goal came after midfielder Tim Cahill leapt over Vidic to head the ball home, prompting Serb media and many fans to say that a player of his stature "should have done better."
The missed penalty against Slovenia, when Serbia needed a win to clinch a Euro 2012 playoff berth, proved to be the final straw for the 30-year old.
"The FSS wishes to thank Vidic for everything he has done for Serbian football...we respect his decision and we wish to underscore the national team's doors will be open for him if he chooses to return," the Serbian FA said.
"We would be honoured to have Vidic back in the national team because Serbia's football is heavily indebted to him for all his accomplishments."
Vidic -- dogged by injury this term -- has won four league titles, one Champions League as well as a FIFA Club World Cup and three League Cups with Manchester United.