WASHINGTON—President Trump said he favors beefed-up background checks for gun buyers, but offered no clarification of his stance amid recent signs he was backing away from stricter rules under pressure from guns-rights activists.

“We are going to be doing background checks. We are going to be working with Democrats, we are working with Republicans,” Mr. Trump told reporters outside the White House on Wednesday. “We already have very strong background checks but we are going to be filling in some of the loopholes,” he said.

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