House Speaker Nancy Pelosi speaks during her weekly news conference on Capitol Hill on May 19, 2022, in Washington, DC.
Washington CNN  — 

House Speaker Nancy Pelosi said next week she will bring forward legislation to ban military-style assault weapons, as the chamber moves to address gun violence.

She said “we will be having a hearing and marking up the assault weapon ban” as soon as the House addresses several pieces of legislation, including the package the House Judiciary Committee will mark up on Thursday.

Speaking at a rally against gun violence in San Francisco, Pelosi said, “We just are trying to hit it in every possible way,” to try and curb mass shootings across the country.

“Of course we want the Senate to pass the background check legislation, which will save more lives than any of the initiatives we have,” she said. The Democratic-controlled House passed legislation to strengthen background checks last year but it’s stalled in the Senate.

The House is also expected to take up a bill by Democratic Rep. Lucy McBath of Georgia, whose son was shot and killed in 2012, which would allow family members and law enforcement to obtain an extreme risk protection order, which temporarily removes access to firearms for those who are deemed a danger to themselves or to others, as well as an Amber Alert-style notification system for when active shootings happen.

“Each one of them is a place where we can save lives. Each one of them is a place where we hope to have bipartisan support to get the job done,” Pelosi said.

The package being considered by the Judiciary Committee, known as the “Protecting our Kids Act,” would likely pass the House but wouldn’t overcome a Republican-led filibuster in the Senate.

The Senate’s discussions revolve around less restrictive gun measures than the House Judiciary Committee’s bill, including strengthening background checks and incentivizing mental health initiatives.

As part of the package of potential changes, senators are looking at strengthening state laws allowing authorities to take away weapons from individuals deemed a risk, known as red flag laws. Leading that part of the discussions are Sens. Richard Blumenthal, a Connecticut Democrat, and Lindsey Graham, a South Carolina Republican.

After Wednesday afternoon’s meeting, Blumenthal released a statement saying talks on that issue, and the safe storage of guns, are moving in a positive direction.

Republican Sen. Susan Collins of Maine, who took part in the bipartisan gun talks, said the two sides were making “rapid progress” toward a deal.

“We are making rapid progress toward a common-sense package that could garner support from both Republicans and Democrats,” she said.

This story has been updated with additional reporting.

CNN’s Manu Raju and Ted Barrett contributed to this report.