On Friday, the House of Representatives passed a bill banning semi-automatic weapons. The legislation is unlikely to pass in the Senate.
Most of the recent mass shootings were carried out with assault weapons.
Pelosi said that an assault weapon ban can work because it has worked before.
Congress didn't re-up the ban on assault weapons a decade later.
The 10-year ban is believed to have prevented 10 mass shootings. An additional 30 mass shootings could have been prevented if the ban hadn't expired.
The previous assault weapons ban is believed to have prevented nine mass shootings.
The ban passed by a wide margin. Six democrats and two republicans voted with the other side.
Six democrats voted no, including Henry Cuellar of Texas, Ron Kind of Wisconsin, Vicente Gonzalez of Texas, and Kurt Schrader of Oregon.
The assault weapons ban was supported by both Fitzpatrick and Jacobs.
The House's passage of a new ban was praised by Sen. Dianne Feinstein.
Feinstein hoped the Senate would pass the bill to end gun violence. The purpose of military-style assault weapons and high-capacity magazines is to kill as many people as possible.
It will take at least 10 Republicans in the Senate to pass a ban.