The US Senate voted 64-34 to advance bipartisan gun-safety legislation on Tuesday, hours after negotiators announced they had reached a deal, with final passage likely later this week.

Backers called the bill, aimed at improving background checks, securing schools and giving states federal funds to combat gun violence, the biggest breakthrough on the issue in decades.

Senator John Cornyn of Texas, the lead Republican negotiator, said the legislation “will help keep our children and our communities safer”. Senate majority leader Chuck Schumer quickly teed up the procedural vote aimed at finishing the bill before senators leave for the July 4 recess at the end of the week...