Michael, 72, told an audience in London over the weekend that Val, his co-star in 1996's The Ghost and the Darkness, was "dealing with exactly what I had," referring to oral cancer.
Val's health has been the subject of persistent speculation since pictures showed him apparently with a tracheotomy tube last year.
"I love Michael Douglas but he is misinformed," Val posted on Facebook on Tuesday, adding that he hadn't spoken to Michael for nearly two years.
"I asked him for a referral for a specialist to get a diagnosis for a lump in my throat which prevented me from continuing a tour of my play Citizen Twain," Val wrote, referring to his one-man show about the author Mark Twain.
"I ended up using a team at UCLA and have no cancer whatsoever. I still have a swollen tongue and am rehabbing steadily."
Commentators have pointed out that while Val insists he is healthy now, he did not deny ever having been struck down with cancer.
The actor acknowledged that his recent silence may have stoked speculation that he was putting his Christian Scientist faith - which stresses the primacy of prayer over medical treatment - ahead of his health.
Val had already issued what appeared to be an oblique denial in a Facebook post promoting a film of his play - saying Mark Twain's "values and spirit live on even now! And I'm sure still standing!"
Fans appeared not to be satisfied, however, prompting Val to be more explicit in the follow-up post.
"Whatever led Michael Douglas to speculate about my health, he's a loving and devoted friend to a privileged group of (talented) people around the world, and I'm sure he meant no harm," Kilmer said.
Two-time Oscar winner Douglas revealed in 2010 that he was battling stage four throat cancer, but beat the disease thanks to a combination of chemotherapy and radiotherapy.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)