Senate Minority LeaderMitch McConnell was one of 14 Republican senators who voted in favor of the bill.
The gun safety bill, which includes federal support for states enforcing "red flag" laws, additional funding for mental health services, and closing the boyfriend loophole, required 60 votes to advance and will now be subject to debate.
The full text can be found here.
Fourteen Republicans voted to advance the bill.
Kevin Cramer of North Dakota didn't vote because he didn't like the way the bill was written.
"Our colleagues have put together a package of popular steps that will help make these horrifying incidents less likely while fully respecting the Second Amendment rights of law-abiding citizens," McConnell said.
The Senate will debate the bill before a final vote takes place in the House.