LOS ANGELES — Studies have long shown that gun violence in PG-13 movies has been rising, sometimes exceeding what is shown in popular R-rated films. Now there is research suggesting that some parents think 13 is too young to see intense shooting, even when it appears justified.

“The findings suggest that parents may want a new rating — that the film industry is taking inappropriate advantage of the PG-13 system,” said Daniel Romer, the lead author of the study, which was set for publication on Monday by the journal Pediatrics. He added, “These movies often get a PG-13 rating by omitting the consequences, such as blood and suffering, and by making the use of gun violence seem justified. But parents of teenagers say that even scenes of justified violence are more appropriate for teens who are at least 15.”

The Motion Picture Association of America, which runs the voluntary domestic film ratings system, declined to comment.

The study, arriving during a renewed national gun debate after the massacre in Parkland, Fla., sought to understand, in part, whether justified gun violence in PG-13 movies was less problematic to parents than the unjustified variety. The researchers, working with support from the Annenberg Public Policy Center at the University of Pennsylvania, showed four 90-second clips of the two types of violence to a national sample of 610 parents who had at least one child between ages 6 and 17.