As TMZ first reported, Fabian Zanzi claims that Travolta exposed himself during a neck massage aboard a Royal Caribbean cruise ... and offered to pay him $12,000 to keep the incident quiet. Zanzi detailed his allegations back on video in June (see below).
In court docs filed yesterday by legal pitbull Marty Singer ... Travolta admits to being on the cruise ... but denies all the allegations of misconduct against him.
Travolta also reiterates his point that Zanzi filed a report with Royal Caribbean over the alleged incident when it happened ... but failed to mention any of the sexual details.
Travolta wants the lawsuit dismissed and for Zanzi to pay his attorney's fees.