Two senators are asking Senate Judiciary Committee Chairman Lindsey Graham Lindsey Olin GrahamSteele Dossier sub-source was subject of FBI counterintelligence probe Hillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Key Democrat opposes GOP Section 230 subpoena for Facebook, Twitter, Google MORE (R-S.C.) to give their "red flag" bills a vote in the wake of last weekend's back-to-back mass shootings.

Sen. Dianne Feinstein Dianne Emiel FeinsteinTrump faces tricky choice on Supreme Court pick The Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Abortion stirs GOP tensions in Supreme Court fight MORE (D-Calif.), the top Democrat on the panel, sent a letter to Graham on Monday asking for a vote on her extreme risk, or "red flag," bill.

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"Given the President’s statement in support for these laws today, I again request that you put the Extreme Risk Protection Order Act on the agenda to be considered as soon as possible," Feinstein wrote in the letter.

Feinstein's bill, which is backed by 25 Democratic senators and Independent Sens. Bernie Sanders Bernie SandersThe Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power Bernie Sanders: 'This is an election between Donald Trump and democracy' The Hill's 12:30 Report: Trump stokes fears over November election outcome MORE (Vt.) and Angus King Angus KingHopes for DC, Puerto Rico statehood rise Government watchdog recommends creation of White House cyber director position Democrats step up hardball tactics as Supreme Court fight heats up MORE (Maine), would allow states to use grants to develop red flag laws that allow family members to petition courts for an order preventing someone from purchasing a gun. The state laws could also let family members petition for an order for law enforcement to remove a firearm.

Sen. Marco Rubio Marco Antonio RubioGOP lawmakers distance themselves from Trump comments on transfer of power McConnell pushes back on Trump: 'There will be an orderly transition' Graham vows GOP will accept election results after Trump comments MORE (R-Fla.) also urged Graham to take up his separate "red flag" bill, noting he had asked the committee to bring it up months ago.

"My bi-partisan 'Red Flag' law was filed 18 months ago & again earlier this year. We asked Senate Judiciary to take it up as few months ago. I hope they will now do so. Identifying & stopping a killer before they act is best way to prevent these tragedies," Rubio tweeted.

Rubio's bill is backed by Sens. Jack Reed John (Jack) Francis ReedWhen 'Buy American' and common sense collide Hillicon Valley: Russia 'amplifying' concerns around mail-in voting to undermine election | Facebook and Twitter take steps to limit Trump remarks on voting | Facebook to block political ads ahead of election Top Democrats press Trump to sanction Russian individuals over 2020 election interference efforts MORE (D-R.I.), Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power Billionaire who donated to Trump in 2016 donates to Biden Credit union group to spend million on Senate, House races MORE (R-Maine) and King, which would also use grants to encourage states to pass "red flag" legislation.

The push for Graham to give the two bills a vote comes as Graham announced on Monday that he would be introducing "red flag" legislation "in the very near future" with Sen. Richard Blumenthal (D-Conn.).

“I spoke with the President this morning about this proposal and he seems very supportive," Graham said earlier Monday.

Graham is one three GOP senators tapped by Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) to do bipartisan brainstorming about potential responses to the mass shootings in El Paso, Texas, and Dayton, Ohio.

"I asked them to reflect on the subjects the president raised within their jurisdictions and encouraged them to engage in bipartisan discussions of potential solutions to help protect our communities without infringing on Americans’ constitutional rights," McConnell said in a statement.

In addition to Graham, McConnell said he spoke with Health, Education, Labor and Pensions (HELP) Chairman Lamar Alexander Andrew (Lamar) Lamar AlexanderGraham: GOP has votes to confirm Trump's Supreme Court nominee before the election The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE(R-Tenn.) and Commerce Committee Chairman Roger Wicker Roger Frederick WickerHillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Key Democrat opposes GOP Section 230 subpoena for Facebook, Twitter, Google Senate panel threatens subpoena for Google, Facebook and Twitter executives MORE (R-Miss.).