Democrats ousted at least 15 House Republicans with “A” National Rifle Association ratings, while the candidates elected to replace them all scored an “F” NRA rating.

“This new majority is not going to be afraid of our shadow,” said Mike Thompson, a California Democrat who is chairman of the House Gun Violence Prevention Task Force. “We know that we’ve been elected to do a job, and we’re going to do it.”

Mr. Thompson, who represents a district in the Napa Valley north of San Francisco, said he plans to introduce legislation mandating universal background checks in the opening weeks of the new Congress.