In the wake of last week’s shooting deaths at a church in South Carolina, President Obama and others have renewed a call to address gun violence in the country. But a leading lawmaker on the issue said Wednesday he doesn’t see gun-related legislation happening at the federal level.

“Honestly, I don’t want to build up any false expectations,” Sen. Pat Toomey, Pennsylvania Republican, said on MSNBC’s “Morning Joe.” “I’m not aware that we’ve got the votes to do what Senator [Joe] Manchin and I attempted.”

Mr. Toomey, along with Sen. Joe Manchin III, West Virginia Democrat, led the push in the U.S. Senate to expand gun-purchase background checks in the wake of the December 2012 school shootings in Newtown, Connecticut. But the legislation, along with other proposals to ban certain military-style weapons and high capacity magazines, failed to overcome a filibuster in April 2013.

“Is it possible that some portion of that, some subset of what we were focused on is possible? Honestly, probably not likely,” said Mr. Toomey, who also said he thinks “background checks” is in a different category than “gun control.”

“But I think the fundamental idea is sound, and I intend to continue discussions with my colleagues to see if there might be some support for some way forward,” he said.

Mr. Toomey accepted the “Sandy Hook Promise Champion Award” this week for his work on the issue.

He said people are in agreement that convicted criminals and people adjudicated mentally unfit shouldn’t have guns.

“Unfortunately, it became controversial to establish a procedure to broaden the background checks,” he said. “I’m very disappointed. I think some people mischaracterized the legislation and that led others to oppose it, but look, I think it’s the right thing to do.”

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