Senate Majority Leader Chuck Schumer told the news conference he would bring it immediately to the floor of the upper chamber for a vote.
"Mitch McConnell's legislative graveyard is over. ... We will have a vote and see where people stand. We have to get it done for the safety of our young people. We are going to win on this issue," Schumer said.
Only two Republicans voted to support the bill and two Democrats opposed it. President Joe Biden also strongly supports the measure.
"The American people are overwhelmingly [for it]. I think 90 percent are on our side and now we will vote to get it through the Senate," Schumer said.
Previously on Thursday morning, the House passed by 227 votes to 203, also largely along party lines, a federal gun control bill closing loopholes that had previously allowed individuals to buy weapons at gun shows, privately through transfers or on the Internet that they then used to commit massacres.
