US senators have announced an agreement on a bipartisan gun violence bill, marking a small but notable breakthrough on gun control in the wake of recent mass shootings.

Nine days after Senate bargainers agreed to a framework proposal – and 29 years after Congress last enacted major firearms curbs – senators Chris Murphy, a Democrat and John Cornyn, a Republican, told reporters on Tuesday that a final accord on the proposal’s details had been reached.

The legislation would toughen background checks for the youngest firearms buyers, require more sellers to conduct background checks and beef up penalties on gun traffickers. It would also disburse money to states and communities aimed at improving school safety and mental health initiatives.

The bill also contains provisions to curb domestic violence, including prohibiting romantic partners convicted of domestic violence and not married to their victim from getting firearms. And it would provide money to the 19 states and the District of Columbia that have “red flag” laws that make it easier to temporarily take firearms from people adjudged dangerous, and to other states that have violence prevention programs.

Lawmakers released the 80-page bill Tuesday evening. The measure is estimated to cost around $15bn, which Murphy said would be fully paid for.

The legislation lacks the far more potent proposals that Joe Biden supports and Democrats have pushed for years without success, such as banning assault-type weapons or raising the minimum age for buying them, prohibiting high-capacity magazines and requiring background checks for virtually all gun sales. Those measures were derailed by Republican opponents in an evenly divided Senate.

But the bill, if enacted, will still represent a modest but telling shift on an issue that has defied compromise since Bill Clinton was president. Congress prohibited assault-type firearms in 1993 in a ban that expired after a decade, lawmakers’ last sweeping legislation addressing gun violence.

Senators have seized on the momentum in the wake of devastating killings in Uvalde, Texas, and Buffalo, New York. Murphy said that after Buffalo and Uvalde: “I saw a level of fear on the faces of the parents and the children that I spoke to that I’ve never seen before.” He said his colleagues also encountered anxiety and fear among voters “not just for the safety of their children, but also a fear about the ability of government to rise to this moment and do something, and do something meaningful.”

This bill, Murphy said, was a partisan breakthrough that would “save thousands of lives.” Before entering the Senate, his House district included Newtown, Connecticut, where 20 children and six staff members perished in a 2012 mass shooting at Sandy Hook elementary school.

“Some think it goes too far, others think it doesn’t go far enough. And I get it. It’s the nature of compromise,” Cornyn said.

But he added, “I believe that the same people who are telling us to do something are sending us a clear message, to do what we can to keep our children and communities safe. I’m confident this legislation moves us in a positive direction.”

The Senate majority leader, Chuck Schumer, said his chamber would begin debating the measure right away and move to final passage “as quickly as possible”.

And in a positive sign about its fate, Senate minority leader Mitch McConnell voiced his support, calling it “a commonsense package of popular steps that will help make these horrifying incidents less likely while fully upholding the Second Amendment rights of law-abiding citizens.”

The National Rifle Association, which has spent decades derailing gun control legislation, said it opposed the measure. “It falls short at every level. It does little to truly address violent crime while opening the door to unnecessary burdens on the exercise of Second Amendment freedom by law-abiding gun owners,” the gun lobby group said.

The measure will need at least 10 Republican votes to reach the 60-vote threshold major bills often need in the 50-50 Senate. Ten Republican senators had joined with 10 Democrats in backing the framework, and Cornyn told reporters that “I think there will be at least” 10 GOP votes for the measure.

What’s uncertain is whether the agreement and its passage would mark the beginning of slow but gradual congressional action to curb gun violence, or the high water mark on the issue. Until Buffalo and Uvalde, a numbing parade of mass slayings – at sites including elementary and high schools, houses of worship, military facilities, bars and the Las Vegas Strip – have yielded only stalemate in Washington.

“Thirty years, murder after murder, suicide after suicide, mass shooting after mass shooting, Congress did nothing,” Murphy said. “This week we have a chance to break this 30-year period of silence with a bill that changes our laws in a way that will save thousands of lives.”