Jagger, 62, issued the statement after British newspaper reports suggested that Scott, a stylist, had angered band members by giving them fashion tips and urging some of them to stop smoking.
"It is completely untrue to say that L'Wren has caused a rift between myself and the rest of the band," Jagger's statement said. "This is all nonsense, everyone has their own style.
"We have not had any disagreements about clothes, smoking or L'Wren, and this is all very hurtful for her," he added.
Jagger insisted his 38-year-old partner, who he has dated for about four years, was close to all the other wives and girlfriends of the band.
"L'Wren would not dream of interfering with a band who have been on the road for 40 years," he said. "In fact the band, their wives and girlfriends are all getting along extremely well."
The Rolling Stones, one of the most successful and influential bands in rock history, are touring North America to promote their latest album, "A Bigger Bang."
In Jagger's statement, the wife of Stones guitarist Ronnie Wood denied that Scott had tried to get her husband to stop smoking.
"Ronnie is the only one who can stop himself from smoking. No one can tell him to stop. Me and L'Wren went together to stop smoking in Boston three years ago," Jo Wood said.
"It's ridiculous about the clothes. Ronnie has the same look which he has had forever and that's not about to change. L'Wren did give some wonderful jackets to Ronnie that I loved and I told her if she found anything else I'd love to see them," she added.
"L'Wren has got great taste, is fantastic company and is just one of the girls on tour."