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Sen. John Cornyn is among a bipartisan group of senators that have drafted legislation to address gun control.

The Texas senator joined "Fox & Friends" Tuesday to address the proposals including proposed "red flag laws," which have drawn criticism from some conservatives.

GOP senators who negotiated this weekend's deal on gun legislation rejected several Democrat proposals, including an assault weapons ban for those under 21, as they helped shape an agreement lawmakers believe can become law.

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Mitch McConnell and John Cornyn

Sens. Mitch McConnell and John Cornyn talk to reporters following a closed-door policy meeting at the Capitol on March 8, 2016. (AP Photo/J. Scott Applewhite, File)

On the controversial "red flag laws," a policy that has faced criticism from Republicans, Cornyn explained that the proposal does not enact national red flag laws, however assists states that do have red flag laws in place. 

"We are, after all, talking about a constitutional right. But the goal is to keep guns out of the hands of people with criminal backgrounds and people with mental health problems, which is the current law," he said.

The senator responded to Missouri Attorney General Eric Schmitt raising concerns on the bipartisan bill Monday night on "Tucker Carlson Tonight." Schmitt denounced "red flag laws" as a step toward eventual gun confiscations.

"Red states like Florida and Indiana have them and they seem to be working relatively well. But again, this is not there's not a national requirement. And certainly one of the requirements of the funding will be the sort of rigorous due process that the attorney general said," Cornyn responded.

Cornyn also explained the need to extend the ban to purchase a firearm to misdemeanor domestic violence offenses. 

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Cornyn said he believes the bill worked on with Democrats strikes the right balance to receive support from both sides of the aisle.

"We've found a way to come up with good policies, enforcing the current law and respecting the right, the fundamental right of law-abiding citizens to keep and bear arms."

Fox News' Tyler Olson contributed to this report