The Arsenal striker was unhappy at being substituted in Holland's 2-1 second round victory against Slovakia in Durban and had been accused of suggesting to Dutch coach Bert van Marwijk that Sneijder should have been the man to be replaced with 10 minutes remaining in the match.
Van Persie has scored just one goal at the finals and has struggled to find his best form following an injury-hit season with Arsenal.
But, Inter Milan ace Sneijder has played down reports of a falling-out with the 26-year-old after they were both reportedly summoned for talks with Van Marwijk following Monday's match.
"Robin assured me that he had not said those words and I have no reason to doubt him," said Sneijder, who went on to score what proved to be the match-winning second goal against Slovakia.
"I don't have a problem with him and I never have done. He was disappointed to come off, that one can understand and it really isn't a serious matter."