Senate Minority Leader Charles SchumerCharles (Chuck) Ellis SchumerSchumer names coronavirus czar candidates in plea to White House Democrats struggle to keep up with Trump messaging on coronavirus Schumer: Fired inspector general will be remembered as a 'hero' MORE (D-N.Y.) is calling on President TrumpDonald John TrumpOvernight Health Care: US hits 10,000 coronavirus deaths | Trump touts 'friendly' talk with Biden on response | Trump dismisses report on hospital shortages as 'just wrong' | Cuomo sees possible signs of curve flattening in NY We need to be 'One America,' the polling says — and the politicians should listen Barr tells prosecutors to consider coronavirus risk when determining bail: report MORE to tell Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellFlorida Democrat hits administration over small business loan rollout The Hill's Coronavirus Report: Dybul interview; Boris Johnson update Schumer says nation will 'definitely' need new coronavirus relief bill 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 MurphyDemocrats seize on Trump's firing of intelligence community watchdog Testing struggles emerge as key hurdle to reopening country Democratic senators call on domestic airlines to issue cash refunds for travelers 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.

Sen. Maggie HassanMargaret (Maggie) HassanDemocrats urge administration to automatically issue coronavirus checks to more people Mnuchin says Social Security recipients will automatically get coronavirus checks Lawmakers press IRS to get coronavirus checks to seniors MORE (D-N.H.) said McConnell should "convene the Senate immediately for an emergency session." Meanwhile, Sen. Mazie HironoMazie Keiko HironoOvernight Health Care: CDC recommends face coverings in public | Resistance to social distancing sparks new worries | Controversy over change of national stockpile definition | McConnell signals fourth coronavirus bill Democratic senators want probe into change of national stockpile description Democratic senators ask IRS to extend tax filing deadline amid coronavirus outbreak MORE (D-Hawaii) said it was "past time" for McConnell to act.

"Call us back for a vote. Now," she added.