The administration has overseen a striking drop in prosecutions of gun crimes, winning only about 6,000 convictions in 2015 — down more than 15 percent from five years ago, and giving added weight to claims by gun rights groups that President Obama has failed to enforce the laws already on the books.

As a series of high-profile mass shootings has drawn attention to the issue, Mr. Obama has pushed for ever-stricter gun laws prohibiting sales of some firearms and paraphernalia, and more controls on whom they can be sold to.

But the push comes as his lawyers at the Justice Department are winning fewer cases using the laws already passed to ban criminals from buying or owning firearms, according to data compiled by the Transactional Records Access Clearinghouse at Syracuse University.

The trend predates Mr. Obama, with convictions peaking at 9,206 a decade ago but dropping to 6,002 in fiscal year 2015 — a fall of more than a third.

Part of the reason is prosecutors are simply bringing fewer cases.

Of the two most common federal gun offenses — illegally selling a firearm or using one in connection with another crime — the number of cases dropped from 11,067 in 2004 to 8,078 in 2014, according to data kept by federal prosecutors. The figure ticked up in 2015, to 8,528, hinting that a rise in convictions could also be on the horizon.

Erich Pratt, a spokesman for Gun Owners of America, said the drop in convictions makes sense because there has been an overall drop in murders — and he credited expanded gun rights for the good news.

“The fact is, armed citizens serve as a deterrent to crime,” he said. “The number of concealed-carry holders has tripled since the time Obama took office, even while the national murder rate has fallen 25 percent.”

But Ladd Everitt, a spokesman for the Coalition to Stop Gun Violence, said gun prosecutions are a bad way to gauge how well gun control is working.

“Prosecutions or not, we still have the weakest gun laws in the free world — by far,” he said in an email. “And we are still seeing one mass shooter after another passing background checks and LEGALLY stockpiling guns despite obvious red flags in their background indicating [a] history of violence.”

The issue of gun control and gun violence has come up frequently this year in the wake of the terrorist attack in San Bernardino, as well as mass shootings at a community college in Oregon and at a Planned Parenthood facility in Colorado.

Mr. Obama and Democrats have used the incidents to call for more gun control, even as advocates acknowledge that more stringent background checks wouldn’t necessarily have stopped such incidents from occurring. But some Republicans have pointed to the level of prosecutions to argue why piling on more legal restrictions isn’t the answer.

Former Hewlett-Packard CEO and 2016 GOP presidential candidate Carly Fiorina said recently that ideology triggers a “knee-jerk” reaction among people on the left to push for more gun controls after mass shootings.

“I actually think it’s ideology, not common sense, that causes the left wing, every time, in a knee-jerk reaction, to say the answer here is more laws when we’re not enforcing the laws we have,” Mrs. Fiorina said on MSNBC’s “Morning Joe.” “Let’s start by enforcing the laws we have.”

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