Senate Majority Leader Harry Reid on Tuesday vowed to move forward with legislation to expand background checks for gun buyers but said he doesn't have enough support yet to hold a vote.

The Nevada Democrat said in light of the fatal shootings at the Washington Navy Yard Monday that killed 13, including the accused shooter, "we're going to move this [legislation] up as quickly as we can."

But he quickly added he only will bring the matter to the Senate floor when he has the 60 votes likely needed to pass the measure, a move he said isn't plausible in the near future.

"We don't have the votes," he said. "I hope we get them, but we don't have them now."

The Senate in April rejected a far-reaching plan that would have expanded background checks on firearms sales and banned some semi-automatic weapons. Minutes after the vote President Barack Obama and Reid vowed to continue the fight.

Reid said he talks to his colleagues "consistently" about revisiting the issue but said he faces daunting resistance from Republicans who oppose gun control.

"The thing that bothers me is a great number of Republicans say, 'Yeah, we know you're right, but we can't do anything about it,'" he said. "So, here we are."

The majority leader said that, for now, he is willing to narrow the scope of a background check bill that would restrict firearm sales to those with mental illness.

"That's something we will look at," he said. "We want to stop people who have mental illness from buying a gun. We want to stop people who are felons from being able to purchase a gun. That's what that's all about."