[cnn-photo-caption image= http://i.cdn.turner.com/cnn/2008/images/04/01/art.pelosiclinton.ap.jpg caption=" Pelosi said Tuesday the presidential race should run its course."]
(CNN) - House Speaker Nancy Pelosi said Tuesday she wants the Democratic presidential election to continue through the last round of primaries, but warned against a floor fight at the party's August convention.
"I think the election has to run its course," Pelosi said, later adding, "I do think it is important for us to get behind one candidate a long time before we go to the Democratic convention if we expect to win in November."
Pelosi's comments come as Hillary Clinton is increasingly suggesting she is willing to take her presidential bid all the way to the Democratic convention at the end of the summer.
"I have no intention of stopping until we finish what we started and until we see what happens in the next 10 contests and until we resolve Florida and Michigan. And if we don't resolve it, we'll resolve it at the convention - that's what credentials committees are for," the New York Democrat told the Washington Post.
In the interview Tuesday, Pelosi said she understands why Clinton is making that argument, since 10 more primary contests remain over the next two months.
"We don't know what these next elections will do. We do not know what the conduct of the campaigns in the next four to six weeks will produce," she said. "So if you are a candidate for president, you certainly are saying that you are going to the convention - you can't say anything but. And Senator Clinton might well be going to that convention as the nominee."
But Pelosi suggested a clear frontrunner will emerge well before the party's convention.
"At some point it'll be clear that there is a frontrunner - and at that point we would hope that, for the greater good, for the country, that we can all rally as early as possible behind one person," she said.
The House Speaker also maintained her argument that the party's superdelegates should not overturn the pledged-delegate outcome, and suggested she wasn't affected by a recent letter from powerful Clinton fundraisers criticizing that stance.
"It wasn't important to me," she said of the letter.
- CNN Ticker Producer Alexander Mooney