Vitter, who is running for re-election, made the comments at a town hall-style event in Metairie, La., on Sunday when a constituent asked what he would do about what the questioner said was Obama's "refusal to produce a valid birth certificate."
With the crowd applauding the question, Vitter responded that he doesn't personally have standing to bring litigation. "But I support conservative legal organizations and others who would bring that to court," he said, according to a video of the event. "I think that is the valid and most possibly effective grounds to do it."
He later cautioned that the matter could distract from policy issues.
"I think if we focus on that issue and let our eye off the ball ... I think that's a big mistake," he said. "I'm not dismissing any of this. I think first and foremost, we need to fight the Obama agenda at the ballot box starting this fall."
So-called birthers have challenged Obama's standing as president by arguing that he was not born in the United States.
Hawaii officials have repeatedly confirmed the president's citizenship, and his Hawaiian birth certificate has been made public, along with newspaper birth notices published when he was born in 1961.
Vitter said the only direct information he has about the issue is what he's learned through the news media "filter." His spokesman did not immediately respond to a question about whether the senator doubts Obama's citizenship.