WASHINGTON — The Supreme Court on Thursday narrowed the reach of the federal Armed Career Criminal Act, a kind of three-strikes statute, ruling by a 5-to-4 vote that violent felonies committed recklessly — as opposed to intentionally or knowingly — do not count as strikes.

The law requires mandatory 15-year sentences for people convicted of possessing firearms if they have earlier been found guilty of three violent felonies. An offense qualifies as a violent felony if it involves “the use, attempted use or threatened use of physical force against the person of another.”

The majority featured an unusual coalition, with Justice Neil M. Gorsuch joining the three-member liberal wing and Justice Clarence Thomas voting with that plurality on different grounds.

The case concerned Charles Borden Jr., who pleaded guilty to a federal gun crime. Prosecutors sought to impose the mandatory 15-year sentence based on three earlier convictions, one of them in Tennessee for reckless assault. That conviction, Mr. Borden argued, should not count as a strike. Lower courts rejected his argument, and he was sentenced under the career-criminal law.

Justice Elena Kagan, writing for four justices, disagreed, saying the law excluded crimes in which the defendant had merely been reckless. The words “against the person of another,” she wrote, requires volitional conduct and “demands that the perpetrator direct his action at, or target, another individual.”

She gave an example to illustrate the difference. Consider, she wrote, a commuter, late for work, who runs a red light and hits a pedestrian. That driver was reckless, she wrote, but “has not directed force at another: He has not trained his car at the pedestrian understanding he will run him over.”

“In ordinary language,” Justice Kagan wrote, “against” means “in opposition to,” giving examples: “The general deployed his forces against a rival regiment, or the chess master played the Queen’s Gambit against her opponent.”