Sneijder was the team's allocated dead-ball taker, only for Van Persie to attempt to wrest the ball from his grasp.
The Real Madrid midfielder, recovering from an injury sustained against Van Persie's Arsenal, told the Dutch newspaper Het Parool that Van Persie has 'broken agreements', and that he wanted a showdown.
Late in the last-eight tie against Russia, the Netherlands were awarded a free-kick, which Van Persie duly took. He missed, but Ruud Van Nistelrooy subsequently scored to take the game to extra time. However, Sneijder has revealed that the Arsenal striker broke team protocol.
Sneijder is quoted thus: "From the first practice game, I've been designated as the man who takes free kicks and no one else is supposed to touch the ball.
The ex-Feyenoord man Van Persie aimed low in his reply: "I expected more class from Wesley,'' he told Algemeen Dagblad.
"Besides, it's absolute nonsense that he's the only one who can take free kicks. You can ask the coach.''
Ex-Netherlands coach Marco Van Basten, in charge at the time of the 3-1 defeat, refused to comment while his replacement Bert Van Marwijk will not speak about the incident until he summons the squad togethet next week for the World Cup qualifying fixtures.
He continued: "I'm flabbergasted by the way Wesley has acted. Must the whole country take part in a 'meeting' between Sneijder and Van Persie?''