EXCLUSIVE

Val Kilmer's family believes the actor is killing himself by not dealing with a serious tumor ... because of his religious beliefs.

TMZ broke the story ... Val was rushed to the hospital Monday night after he started bleeding from the throat. Doctors at UCLA Medical Center, Santa Monica operated immediately and found a tumor. We're told the surgery was invasive ... they needed to enlarge a path to facilitate breathing.

Family members tell TMZ ... Val has known about the tumor since Summer. He had trouble speaking and his neck swelled to the point he covered it up with scarves and other clothing items.

The family members say they urged Val to seek treatment but he would have none of it because of his Christian Science beliefs. They say he shunned medical treatment and anyone who persisted got cut out of his life.

Christian Science followers generally believe prayer heals, not medical treatment.

The family says Val would never confess to pain because it was an admission that prayer didn't work, but when he started coughing up blood Monday his options ran out.

The family is hopeful because Val seems somewhat more receptive to treatment.