Senate Minority Leader Charles SchumerChuck SchumerFirst Black secretary of Senate sworn in Republican Ohio Senate candidate calls on GOP rep to resign over impeachment vote The bizarre back story of the filibuster MORE (D-N.Y.) is calling on President TrumpDonald TrumpProsecutors focus Trump Organization probe on company's financial officer: report WHO official says it's 'premature' to think pandemic will be over by end of year Romney released from hospital after fall over the weekend MORE to tell Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellJudiciary Committee greenlights Garland's AG nomination This week: Senate takes up coronavirus relief after minimum wage setback Juan Williams: Hypocrisy runs riot in GOP MORE (R-Ky.) to bring up a stand-alone background check bill, dismissing Trump's suggestion of tying it to immigration reform.

"Instead of flailing around blaming everything under the sun, if the president is serious about 'strong background checks' there’s one thing he can do: Demand Sen. McConnell put the bipartisan, House-passed universal background checks bill up for a vote," Schumer tweeted on Monday.

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Trump said on Monday that he wants legislation providing "strong background checks," including potentially linking it to long-stalled immigration reform. Background check legislation already faces an uphill climb in the GOP-controlled Senate, but tying it together with immigration legislation would all but guarantee it would not get passed.

Talk of new background check legislation comes after two mass shootings rocked the nation over the weekend.

A gunman on Saturday killed 20 people and wounded dozens more in an attack at a Walmart in El Paso, Texas, on Saturday. Less than a day later, at least nine people were killed and more than two dozen were injured in a Dayton, Ohio shooting. The two shootings are not believed to be linked.

Democrats are trying to build pressure on McConnell to bring up background check legislation after the two shootings, including calls for the GOP leader to bring the Senate into session during the August recess.

The Senate left for the five-week August recess on Thursday and are out of session until Sept. 9. A spokesman for Schumer didn't immediately respond to a question about if Democrats will try to clear a bill by unanimous consent during pro forma sessions this week. The request would likely be blocked by a GOP senator.

Sen. Chris MurphyChristopher (Chris) Scott MurphyAmazon manager sues company over racial discrimination, harassment allegations Overnight Defense: Biden sends message with Syria airstrike | US intel points to Saudi crown prince in Khashoggi killing | Pentagon launches civilian-led sexual assault commission Minimum wage setback revives progressive calls to nix Senate filibuster MORE (D-Conn.) echoed Schumer's demand during a tweet on Monday morning saying Trump asking McConnell to bring up a bill would ensure its passage.

"Background checks has already passed the House - w Republican votes. If Trump asked McConnell to support it, it would pass in a week. FYI - he won’t do that," he tweeted.