Now in remission, Kilmer answered fans questions on Reddit on Tuesday - and insisted prayers from friends, family and fans defeated the incurable disease.
The book of poems is difficult to obtain, and expensive; even second-hand copies fetch $300 and up.
His big break came when he received top billing in the comedy spoof of spy movies Top Secret! Kilmer sang all the songs in the film and released an album under the film character's name, "Nick Rivers." Following roles in the television films The Murders in the Rue Morgue and The Man Who Broke 1,000 Chains, Kilmer played Madmartigan in the fantasy Willow; he met his future wife, co-star Joanne Whalley, on the film's set.
"friends said it's official - #TOPGUN2 was announced today.
" the actor posted alongside a photo of himself wearing a t-shirt featuring his character Iceman.
At the time, Michael Douglas said Kilmer was "dealing with" throat cancer, a disease Douglas himself was diagnosed with in 2010.