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Pelosi says House will consider legislation banning assault weapons

She said “we will hold a hearing and note the ban on assault” as soon as the House of Representatives considers several pieces of legislation, including the package that the House Judiciary Committee will mark on Thursday.

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

“Of course, we want the Senate to pass legislation to check the past, which will save more lives than any of the initiatives we have,” she said. The Democrat-controlled House passed legislation to step up inspections last year, but it is stagnant in the Senate.

The House is also expected to pass a bill by Georgia lawmaker Lucy McBatt, whose son was shot and killed in 2012, that will allow family members and law enforcement officials to receive an emergency risk protection order that temporarily removes access to firearms for those who consider themselves a danger to themselves or others, and an Amber Alert-style notification system when active shootings occur.

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

The package, which is being considered by the Judiciary Committee, known as the “Protection of Our Children Act,” is likely to pass the House of Representatives, but will not overcome the Republican-led filibuster in the Senate.

Senate debates revolve around less restrictive weapons measures than the House of Representatives bill, including stepping up background checks and boosting mental health initiatives.

As part of a package of potential changes, senators are considering strengthening state laws that allow authorities to confiscate weapons from individuals considered risky, known as red flag laws. Leaders in this part of the debate are Senator Richard Blumenthal, a Democrat from Connecticut, and Lindsay Graham, a Republican from South Carolina.

Following the meeting on Wednesday afternoon, Blumenthal issued a statement saying talks on the issue and the safe storage of weapons were moving in a positive direction.

Republican Sen. Susan Collins of Maine, who is involved in the bipartisan arms talks, said the two sides were making “rapid progress” toward the deal.

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

This story has been updated with additional reports.

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