Granada host Real Madrid in La Liga on Saturday and Marca, which has stood by its story, quoted Caparros as saying in its Friday edition: "I only ask that they do not steamroller us".
Caparros hit back angrily at the paper at a pre-match news conference, saying he would never have said anything like that and expressing his disgust at the article.
"Experience tells me not to read the press or listen to anything and that's what I do but when there is a headline like this," he said, brandishing Marca's front page.
"You think I could have made these comments? How do you think I can motivate my players?" he asked assembled reporters, before ripping the page into small pieces and flinging them on the table in front of him.
"People who know me know that I would not gift anything to anyone, even to my father, who is in heaven and is what I love most in the world," Caparros fumed.
"I have been working in football for many years and these kinds of headlines piss me off.
"How can I go into the dressing room to the players? We already had it tough but on top of that they want to divide us."
IMMEDIATE RECTIFICATION
Enrique Ortego, the journalist who interviewed Caparros by telephone for the article, insisted he had quoted the coach accurately.
"He knows that he said it and I know that he said it," Ortego wrote on Marca's website (www.marca.com).
"What deserves an explication is his reaction and behaviour in the press room ripping up the front page of Marca and questioning the paper," he added.
"It's playing with the credibility of a newspaper and its workers and requires an immediate rectification.
"The truth is the truth and you can't manipulate it even in an attack of rage."
Real coach Carlo Ancelotti expressed a degree of sympathy for Caparros when asked about the incident on Friday.
"I have felt like ripping up a newspaper many times, so I understand very well what Caparros did. He would have done it with relish," Ancelotti told a news conference.
"These things can happen, although I have never destroyed a paper."
Granada are 14th in the La Liga standings after nine matches, 12 points behind third-placed Real.
(Reporting by Iain Rogers, editing by Ian Chadband)
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