The owners of the dive boat that caught fire off the coast of Southern California, killing 34 people aboard, say they shouldn’t have to pay a dime to the victims’ families, according to a new report.

Glen and Dana Fritzler have cited an obscure maritime law from 1851, the Limitation of Shipowners’ Liability Act, in arguing that they shouldn’t financially be on the hook for the tragedy, the Los Angeles Times reported.

The couple, who own the 75-foot vessel named Conception through their company Truth Aquatics Inc., filed court papers in California federal court on Thursday — as authorities struggle to positively identify the bodies recovered from the early morning blaze just days earlier.

The boat, which had 33 passengers and six crew members on board, burst into flames around 3:15 a.m. Monday. Five crew members managed to escape — but one member and all of the passengers who were asleep below deck were trapped by the blaze and couldn’t make it out.

All but one body has been recovered.

The vessel was completely engulfed and is now considered a total loss with “zero residual value,” the filing obtained by The Post said.

“The Fire and all consequential alleged injuries, damages and deaths occurred without the privity or knowledge on the part of Plaintiffs, and was not caused or contributed to by any negligence, fault or knowledge on the part of Plaintiffs, or anyone for whom Plaintiffs may be responsible, at or prior to the commencement of the above-described voyage,” the court papers said.

No lawsuits have been filed by victims or families of victims — but the Fritzlers said they’ve received notices that some may be forthcoming, according to the filing.

In order to win the suits, the couple would have to prove that their company wasn’t responsible for the fire.

The cause of the fire is under investigation.

The victims had just wrapped up a three-day diving excursion of San Miguel Island and were set to return to Santa Barbara Harbor Monday evening.

Philadelphia-based maritime lawyer Robert Mongeluzzi called the Fritzlers’ legal maneuver predictable — but cold-hearted.

“It is pretty heartless when not all the bodies have been recovered to file something saying their lives are worthless,” he told the LA Times.

Russell Brown, who represents Truth Aquatics, did not immediately return an email from The Post.