Dr. Donal Billig, the former heart surgeon from Bethesda Naval Hospital who was sentenced to four years in prison for the deaths of three patients, was denied parole last week by the Navy.

Chase Untermeyer, assistant secretary for manpower, accepted a recommendation made July 9 by the Naval Clemency and Parole Board to deny Billig's request for parole. The parole board made its recommendation after a prison board hearing at Fort Leavenworth, Kan., where Billig was sent after his conviction in March 1986, a Navy spokesman said.

Billig, 56, was sentenced to four years in prison after a general court-martial in which he was found guilty of the involuntary manslaughter of two patients and the negligent homicide of a third in 1984. His trial was only the second time a Navy doctor had been accused of killing a patient through culpable negligence.

Billig was eligible for parole after 16 months at Fort Leavenworth, where he is doing farm work.

According to Navy records, 32 claims have been filed, asking for a total of $141.7 million in damages for injuries and deaths connected to operations undertaken by Billig. Seven claims have been settled, totaling $1.22 million, Navy spokesmen said yesterday.