Sen. Chris Murphy Christopher (Chris) Scott MurphyDemocratic senator calls for 'more flexible' medical supply chain to counter pandemics The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon GOP chairman to release interim report on Biden probe 'in about a week' MORE (D-Conn.) said Thursday he is convinced support for stronger background checks is not off the table after he spoke to White House officials.

"I spoke with the White House today. They have not walked away from improving background checks," Murphy tweeted. "I am skeptical we can reach consensus but I’m willing to stay at the table over next few weeks. Maybe I’m a fool for trying but stakes are too high."

I spoke with the White House today. They have not walked away from improving background checks. I am skeptical we can reach consensus but I’m willing to stay at the table over next few weeks. Maybe I’m a fool for trying but stakes are too high. — Chris Murphy (@ChrisMurphyCT) August 22, 2019

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The White House declined to comment on President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE's call with Murphy, who has been a leading advocate for more gun control laws since the Sandy Hook Elementary School massacre in his state in 2012. The senator first spoke with the president on the subject last week.

Mass shootings earlier this month in Dayton, Ohio, and El Paso, Texas, left 31 people dead and renewed debate over stronger gun laws.

Trump has taken a range of positions publicly on what he supports after the latest mass shootings. But his most recent comments emphasizing the need to address mental health, highlighting existing laws and talking about the "slippery slope" of enacting new gun laws raised questions about whether he'd abandoned support for background checks.

The president insisted to reporters on Thursday that he has an "appetite" for background checks.

But Trump later qualified his comments to say he hoped to close loopholes in the system, and reiterated he was concerned that Democratic demands may go too far and doom an agreement.

"We're working on background checks," he said. "There are things we can do. But we already have very serious background checks."

The White House legislative affairs team has taken the lead in negotiations with lawmakers, and administration officials have described talks as ongoing even amid outside skepticism that the president will follow through.

But pro-gun groups and White House allies have cautioned that Trump risks support among his base if he pushes through laws that restrict access to firearms, and the National Rifle Association has pushed back against proposals that have been made public.