House panel approved a significant funding increase to improve background checks on gun sales.

Gun control supporters made progress in both chambers this week, as a Senate committee advanced a nominee to become the first permanent director of the Bureau of Alcohol, Tobacco, Firearms and Explosives in seven years and a House panel approved a significant funding increase to improve background checks on gun sales.

In the House, the prospects may be more encouraging for gun control supporters after an Appropriations subcommittee on Wednesday approved a spending bill for Commerce, Justice and science-related agencies that includes $55 million for states to improve the National Instant Criminal Background Check System, the database gun dealers use to determine whether prospective buyers are dangerous and should be turned away.

Mayors Against Illegal Guns, the gun control advocacy group co-founded by New York City Mayor Michael R. Bloomberg, praised the bipartisan funding increase and said it amounts to more money for the background check program “than has been appropriated in the previous four years combined.”

Rep. Frank R. Wolf, the Virginia Republican who chairs the subcommittee, said in a letter to his constituents Friday that the additional money for background checks — together with other funding for school safety improvements — are “tangible and significant steps toward reducing gun violence.”

Wolf said his efforts to expand funding for background checks began before recent shootings in Connecticut and Aurora, Colo., but that those attacks have “made the need for increased funding all the more important.”