Cruise, during a famously heated debate on NBC's "Today" show in 2005, criticized Brooke Shields for taking anti-depression drugs and berated host Matt Lauer for suggesting that psychiatric treatment might help some patients.
"I don't disagree with anything Tom says," Travolta says in the July issue of W magazine, on newsstands Friday. "How would I have presented it? Maybe differently than how he did, but it doesn't matter. I still think that if you analyze most of the school shootings, it is not gun control. It is (psychotropic) drugs at the bottom of it."
"I don't want to create controversy; I just have an opinion on things, and there is nothing wrong with stating your opinion if you are asked," he continues. "Everyone wants that right, and because you are famous doesn't mean you have less of a right."
Travolta, who also talks of his habit of going to bed at 6 or 7 in the morning and waking in the early afternoon, says being famous has little impact on how he lives his life.
"I will tell you the things that would be the same, fame or no fame," he says. "Being up all night would be the same. Liking empty restaurants, liking empty movie theaters — unless I am starring in it."
Travolta, 53, portrays Ms. Edna Turnblad in "Hairspray," the adaptation of the stage musical that was spun from the 1988 John Waters film of the same name. The new film opens July 20. The role, in which he dons a fat suit and feminine garb, has added fuel to ongoing speculation about his sexuality.
"I have never been compelled to share with you my bathroom habits or share with you my bedroom habits," says the married father of two. "Everyone has a right to privacy, so I have never felt — even though I am famous — that I had to share that with anybody."
Do the rumors bother him? Does he think they've affected his career?
"No and no," he says. "What affects your career is the quality of the product. I don't think anyone can hurt me."