U.S. Senators from both parties need to negotiate on bipartisan gun legislation without the involvement of President Biden, Democratic U.S. Sen. Chris Murphy said Sunday.

Murphy, a Democrat from Connecticut, insisted that lawmakers work out the deal on their own when asked during an appearance on CNN’s "State of the Union" if it would be helpful if Biden got involved. 

"I think the Senate needs to do this ourselves," Murphy said. "I've talked to the White House every single day since these negotiations began, but right now the Senate needs to handle these negotiations."

Both Republicans and Democrats are talking about possible changes to gun laws following several mass shootings in recent weeks, including the shooting at an elementary school in Uvalde, Texas, that left 19 children and two teachers dead.

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Sen. Chris Murphy, D-Conn., a gun control advocate, spoke about how a bipartisan group of senators is considering how Congress could make meaningful gun reforms. (AP Photo/J. Scott Applewhite)

Murphy described the bipartisan negotiations as the most serious he’s ever been a part of, saying, "There are more republicans at the table talking about changing our gun laws and investing in mental health than at any time since Sandy Hook," where a gunman killed 20 children and six adults at an elementary school in 2012.

Murphy said that among the Republicans working on the potential bill is Sen. John Cornyn of Texas, who he said has talked about looking at how juvenile records are accessed for young men ages 18 to 21 to make sure any who have had previous problems with the law are unable to get a weapon.

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FILE - In the aftermath of recent horrific mass shootings in Uvalde, Texas, and Buffalo, New York, a bipartisan group of senators, including Sens. John Cornyn, R-Texas, pictured right, and Chris Murphy, D-Conn., are working to try to strike a compromise over gun safety legislation. (AP Photo/J. Scott Applewhite, File)

On whether the Senate would put forth a vote on any potential gun legislation this week, Murphy said that while he isn’t sure anything will be voted on, he believes lawmakers need to have concepts to present to their colleagues in the coming week.

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"We're not going to put a piece of legislation on the table that will ban assault weapons or pass comprehensive background checks," Murphy said. "Right now, people in this country want us to make progress, they just don't want the status quo to continue for another 30 years."

Despite the promise of bipartisan gun reform, Murphy said that he’s also been part of many failed negotiations in the past, adding that he’s remaining "sober-minded about our chances."