WASHINGTON — (CNN) The Republican-led House will vote next week on a bill to prevent people on the terrorism watch list from buying guns, Speaker Paul Ryan announced Thursday on a conference call with his GOP members.

Ryan said it’s “just common sense” to make sure “suspected terrorists can’t get guns,” according to a source on the call.

But he said also that he wants to look at the issue deliberately to ensure people’s due process is protected if they don’t believe they should be on the watch list.

The decision comes after Democrats launched a disruptive sit-in on the House floor to protest the lack of legislative action on gun control in the wake of multiple mass shootings in recent months, including the murder of 49 people at a gay nightclub in Orlando earlier this month.

Democrats have vowed to continue their high-profile protest when the House returns next week from its July Fourth recess.

On the call, Ryan said the House would vote on a “terrorism package” that includes measures to “disrupt radicalization and recruitment” as well as preventing people who the government suspects of being terrorists from buying firearms.

Ryan announced the House will vote also next week on a mental health bill from Rep. Tim Murphy, R-Pennsylvania, which is not directly related to gun control but seeks to improve mental health services across the country.

Since many mass shootings are carried out by people with mental health problems, addressing that complex issue has been a priority for members of both parties.

Details of the anti-terror legislation were not immediately available so it wasn’t clear if Democrats would support the measures.

Last week, the Senate rejected a series of gun-related measures from both parties, including one from Democrat Dianne Feinstein of California to prevent people on the government’s watch list from purchasing firearms.

Since then, Sen. Susan Collins, R-Maine introduced a similar — but scaled back — bill, on which she is working to build bipartisan support for in the weeks ahead.

The same bill was introduced in the House by Republican Rep. Carlos Curbelo of Florida.

On the issue of the Democratic protests, which Ryan had dismissed as “publicity stunts,” the speaker told his GOP members that the leadership was gathering facts, evaluating options and getting recommendations from the parliamentarian and Sergeant at Arms about what to do if the protests continue to interrupt floor action.

Ryan said GOP leaders will take any action they deem necessary.