The U.S. Senate’s top Democrat called a bipartisan gun control proposal from Republican Sen. Susan Collins of Maine “a step in the right direction” on Wednesday and urged a floor vote on the measure.

Senate Minority Leader Harry Reid, D-Nev., initially stopped short of endorsing Collins’ proposal Wednesday morning, but later told Politico that “even though I don’t think everything’s right about it, I would vote for it.” Reid could play a role in bringing additional Democrats on board as Collins and her supporters attempt to draw the 60 votes needed to move the bill forward.

Collins and a bipartisan group of senators unveiled the proposal Tuesday, saying it would prohibit those on the federal “no-fly” list as well as a separate “selectee” list from purchasing firearms. The proposal could come up for a vote on the Senate this week. In a floor speech Wednesday morning, Reid said that although the Collins-led proposal “is not perfect,” he was encouraged by the dialogue over gun safety in the Senate.

“Democrats and Republicans are working together to find solutions and protect Americans from gun violence,” Reid said. “The obvious first step is to keep guns and explosives out of the hands of suspected terrorists and criminals. That’s why it’s imperative that Senator Collins’ legislation get a vote. The amendment from the senior senator from Maine has bipartisan support. At the very least, it’s a step in the right direction.”

Senate Majority Leader Mitch McConnell, R-Ky., had indicated Tuesday that the Senate would likely vote on the proposal.

Collins’ plan would prohibit those on the federal “no-fly” and “selectee” lists from purchasing a firearm. Those on the selectee list are allowed to fly after intensive screening. The bill includes a five-year look-back provision to alert the FBI to gun purchases by someone who had been on the broader Terrorism Screening Database, and would allow anyone on the lists who is prohibited from buying a gun to appeal.

The proposal would affect about 2,700 Americans currently on the two lists. While it has bipartisan support in the Senate, securing passage in the Republican-controlled House will be more difficult given the opposition from the National Rifle Association.

A bipartisan group of senators unveiled the proposal one day after the Senate failed to reach the required 60-vote threshold to move forward with four gun control measures – two sponsored by Democrats and two by Republicans – that have become the primary focus on Capitol Hill after a mass shooting that killed 49 inside a nightclub in Orlando, Florida, this month. Joining Collins during the Tuesday news conference were Sen. Angus King, a Maine independent; Sen. Lindsey Graham, R-S.C.; Sen. Kelly Ayotte, R-N.H.; Sen. Tim Kaine, D-Va.; Sen. Bill Nelson, D-Fla.; Sen. Martin Heinrich, D-New Mexico; and Sen. Jeff Flake, R-Ariz.

During his floor speech, Reid also praised Maine’s senators – both past and present – for their bipartisan work on issues. He credited Collins and former Republican Sen. Olympia Snowe with casting the two decisive votes to allow passage of President Obama’s stimulus package during the 2009 recession. And he called King, an independent who caucuses with the Democrats, “a terrific senator.”

“So it should be no surprise to anyone that the senior senator from Maine is working on a bipartisan basis,” Reid said.