Warner -- in a speech accepting the party nomination for the U.S. Senate -- told an audience in Hampton, Va., he is "110 percent committed" to the Senate campaign, The Washington Post reported.
Some political observers have said the Democratic ticket could have a realistic chance of winning Virginia in November, and attention has focused on Warner as a possible vice presidential nominee. Virginia Gov. Timothy Kaine and Sen. James Webb have also been mentioned as possible running mates.
Warner is running against another former governor, Republican Jim Gilmore, for the Senate seat being vacated by the retirement of Republican John Warner.
"Let me be clear about this: I have been working very hard these last few months to ask the people of Virginia to give me the honor of being their United States senator," Warner said Saturday. "I will not seek, and I will not accept, any other opportunity."