An unusual bipartisan effort in the United States Senate to agree on legislation to confront a string of mass shootings garnered a commitment for swift action on Thursday, as legislators reported progress toward a resolution.

A group of legislators led by Democratic Senator Chris Murphy and Republican Senator John Cornyn is attempting to reach an agreement on a plan to improve school security, suggest remedies in the existing US mental health system, and keep guns out of the hands of criminals and individuals considered a threat to the public or themselves.

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Senate Majority Leader Chuck Schumer said the negotiations were making “good progress” and that a deal might be reached “very soon.”

“As soon as the bipartisan group comes to an agreement, I want to bring a measure to the floor for a vote as quickly as possible,” Schumer stated in a floor speech.

Negotiators and aides suggested a deal in principle might be reached later Thursday. However, lawmakers would have a better idea of the breadth of future conversations before departing Washington for the weekend.

“We’ll have a better idea of whether we still have momentum, which I believe we do right now,” Cornyn informed reporters on Wednesday.

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Murphy told reporters that he hoped to enact legislation to curb the stream of fatal shootings in America before the Senate adjourned for the July 4 holiday at the end of the month. “This would be a big, historic deal, and we need to get it right,” he said.

The initiative comes in the wake of recent shooting incidents in Buffalo, New York, Uvalde, Texas, Tulsa, Oklahoma, and other cities.

Democrats, including President Joe Biden, have called for tighter restrictions on gun ownership, including one with a ban on semi-automatic, assault-style rifles and high-capacity magazines, as well as an increase in the minimum age to purchase such weapons from 18 to 21.

The Democratic-controlled House of Representatives approved a broad gun-control bill late Wednesday, mostly along party lines.

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However, that bill has little chance of passing in the Senate, which is evenly split between Democrats and Republicans. Republicans have consistently defended gun ownership rights as a party.

Instead, lawmakers are exploring very minor tweaks that could garner the 60 votes required for passage in the Senate’s 100-seat chamber.

Discussions about expanding mental health services and rewarding state “red flag” laws to keep guns out of the hands of certain individuals have turned to how to offer possibly billions of dollars in financing without increasing the federal deficit.

Lawmakers are also debating legislation to improve school physical security, such as more on-campus security personnel, and suggestions to include juvenile records in national background check repositories.