The RadioShack Nissan Trek team leader said he "formally rejects" having taken any banned substance, and requested the B sample to be tested.
"If this analysis confirms the first result, a complaint will be filed against an unspecified person for poisoning," the rider said in a statement on Wednesday.
A RadioShack spokesman confirmed the authenticity of the statement to The Associated Press. The team pulled Schleck from the Tour on Tuesday after the positive test, and said he would be suspended if the backup sample comes back positive, too.
He's the older brother of Andy Schleck, the 2010 Tour champion who didn't enter this year because of a spinal injury. Frank was third last year.
"We have faith in Frank, but we can't explain," said RadioShack spokesman Philippe Maertens.
Cycling's governing body the UCI said that Schleck tested positive for the banned diuretic Xipamide on Saturday in a reminder that doping allegations continue to tarnish the image of cycling.
The diuretic is classified as a specified substance and does not require a provisional suspension. The World Anti-Doping Agency defines "specified substances" like Xipamide as those that are "more susceptible to a credible, non-doping explanation."
Bans for such substances are often shorter, and athletes have a better chance of proving that they did not intend to consume it or enhance their performance.
Athletes who dope often take diuretics like Xipamide to mask other banned performance-enhancing drugs, or as a supplement for weight loss, according to the "Dictionary of Doping" by Jean-Pierre de Mondenard, a French expert.
The Katusha team yanked Russian rider Alexandr Kolobnev from the Tour last year after he tested positive for the diuretic Hydrochlorothiazide. However, the Court for Arbitration in Sport ruled earlier this year that the positive test was "justified by medical reasons totally unrelated to sport performance."
American rider Chris Horner defended his RadioShack teammate, saying he was convinced of Schleck's innocence.
"It's questionable on where that particular drug could come from," Horner said. "I don't believe that Frank took it on purpose, that's for certain. Let me say something different - I don't believe he knowingly took it, so I think he will be back with the team as soon as he can clear this up."
RadioShack sports director Alain Gallopin said Schleck's withdrawal from the race will allow the rest of the team to focus on the race and reach Paris, where the Tour ends Sunday.
"Frank needs time to organize his defence," Gallopin said ahead of the start of the 16th stage between Pau and Bagneres-de-Luchon.
"He was really down, as the rest of us. Now we need to move forward. My job as sports director is to motivate my riders by making them keep Frank in their thoughts," Gallopin said.
German veteran Jens Voigt, who is riding in his last Tour, said Schleck apologized to his teammates but was unable to give them an explanation for his positive test.
"We were shocked and surprised," Voigt said. "There was a moment of silence and we have been left trying to digest the news and to start thinking about what it means, the consequences it has or could have, and how we keep going in this situation.
"He said, 'I'm sorry, I don't understand, but I wish you all the best until Paris,'" Voigt said.
Under UCI rules Schleck could have raced on Wednesday, Tour chief Christian Prudhomme said before riders headed into the Pyrenees.
It was better he decided not to, he added in a brief statement.
"It is a wise decision, and for that matter, the only one imaginable," Prudhomme said.
Schleck was in 12th place overall, 9 minutes, 45 seconds behind leader Bradley Wiggins on Tuesday, a rest day on the Tour.
His brother, Andy Schleck was awarded the 2010 Tour title after Alberto Contador was stripped of the win because he had tested positive for clenbuterol.
Associated Press writers Jamey Keaten and Greg Keller contributed to this report.Suggest a correction