"It's only a matter of time before we bring this anti-gun-violence measure back to the floor for a vote," Reid said Thursday. "The stand of the Republicans is not sustainable."
Reid said tabling the gun-control bill would allow the Senate to step over procedural hurdles when it returns to the measure after more behind-the-scenes negotiations, The Hill reported.
Among other things, Reid filed a motion to end debate on a bill that would allow states to collect online sales taxes. The Senate is likely to begin votes on that bill next week.
On Wednesday, the Senate voted 54-46 in favor of the bipartisan amendment from Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa., that would have expanded background checks to all online and gun-show sales. The amendment required 60 votes for approval.
"But make no mistake: This debate is not over," Reid, D-Nev., said on the Senate floor Thursday. "This is not the end of the fight. Republicans are in an unsustainable position -- crosswise with nine out of 10 Americans."
Democrats called for stricter gun laws after a gunman killed 20 first-graders and six educators at Sandy Hook Elementary School in Newtown, Conn., before committing suicide in December. Before heading to the school, Adam Lanza killed his mother, who owned the guns.
Reid commended Manchin, Toomey and other senators for bridging the partisan gap to negotiate the compromise.
"Unfortunately, the overwhelming majority of Senate Republicans ignored the voices of an overwhelming majority of Americans," Reid said from the well. "Yesterday, the families of gun violence victims watched as Republicans defeated a common-sense proposal to expand background checks that has the support of 90 percent of Americans."
Speaking at the White House after the vote, President Obama said senators who voted no "caved" to pressure from the National Rifle Association and said the NRA "willfully lied" about what the legislation would do.
"All in all, this was a pretty shameful day for Washington, but this effort is not over," the president said.