Senate Majority Leader Mitch McConnell – a Republican who has been lambasted by Democrats for refusing to allow votes on gun control legislation – said Monday he is willing to consider “bipartisan” solutions in the wake of the mass shootings in El Paso, Texas, and Dayton, Ohio, but made clear his opposition to gun control policies that infringe “on Americans’ constitutional rights.”

“Today, the president called on Congress to work in a bipartisan, bicameral way to address the recent mass murders which have shaken our nation,” McConnell said in a statement. “Senate Republicans are prepared to do our part.”

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He did not specifically detail the type of legislation he would support. But McConnell’s comments come amid a bipartisan effort from GOP Sen. Lindsey Graham of South Carolina and Democratic Sen. Richard Blumenthal of Connecticut for a bill that would create a federal grant program to assist states in adopting so-called “Red Flag” laws.

In his statement, McConnell said he has spoken with Senate committee leaders and “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.”

“Only serious, bipartisan, bicameral efforts will enable us to continue this important work and produce further legislation that can pass the Senate, pass the House, and earn the president’s signature," McConnell said. "Partisan theatrics and campaign-trail rhetoric will only take us farther away from the progress all Americans deserve.”

The back-to-back mass shootings this weekend have left at least 31 dead and more injured.

The Graham-Blumenthal bill would “assist and encourage” states to adopt Red Flag laws to “timely intervene in situations where there is an imminent threat of violence.”

“These grants will be given to law enforcement so they can hire and consult with mental health professionals to better determine which cases need to be acted upon,” Graham said Monday. “This grant program also requires robust due process and judicial review. It does allow for quick action.”

Blumenthal in a statement Monday said that he and Graham have been working on developing an “Emergency Risk Protection Order” statute since the last Congress.

“We will be finalizing details for this bill and reaching out to colleagues on both sides of the aisle in the coming days and weeks,” Blumenthal said. “I look forward to introducing final legislation with Senator Graham in the very near future.”

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Graham said that he spoke with President Trump about the legislation on Monday morning and said “he seems very supportive.”

Graham and Blumenthal’s announcement came after Trump called for reforms Monday from the White House on mental health and gun laws.

Some Democrats have directed their ire at McConnell – who has refused votes on Democrat-supported gun control language that has passed in the House.

"Mitch McConnell needs to get off his a-- and do something,” Democratic Rep. Tim Ryan of Ohio, a longshot candidate for president, said in an interview on CNN.

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Democratic leaders in Congress on Monday called on McConnell to allow a vote in the GOP-controlled Senate on Democratic legislation, and some have additionally called for cutting the summer recess short to address gun violence.

“In February, the new Democratic House majority promptly did its duty and passed the Bipartisan Background Checks Act of 2019, which is supported by more than 90 percent of the American people and proven to save lives,” House Speaker Nancy Pelosi, D-Calif., and Senate Democratic Leader Chuck Schumer, D-N.Y., said in a joint statement after Trump’s speech. “However, Senate Republican Leader Mitch McConnell has called himself the ‘grim reaper’ and refuses to act on this bipartisan legislation.”

They added: “It is incumbent upon the Senate to come back into session to pass this legislation immediately.”

Brooke Singman contributed to this report.