More than half the country—55 percent—still supports the death penalty, but that’s the lowest level of national support for the punishment in 45 years, according to a new report.

Death sentences and executions are also near historic lows, the report, from the Death Penalty Information Center, said. The center doesn’t officially oppose the death penalty, but its criticism of the way it’s administered often lines up with groups that do.

The recent drop in support for the penalty was greater among Republicans than Democrats, the report said, citing Gallup poll data.

The center’s report also pointed to...