WASHINGTON (Reuters) - Former Massachusetts Governor Mitt Romney has regained his status as front-runner in the race for the Republican presidential nomination and one-time pizza executive Herman Cain has tripled his support to reach third place, a Fox News poll said on Wednesday.

As Republicans reacted to the three debates this month, Texas Governor Rick Perry slipped to second place with the support of 19 percent, a drop of 10 percentage points from a month ago, the poll of Republican primary voters found.

Perry became the instant front-runner when he launched his presidential campaign in mid-August, but his support has faded amid lackluster debate performances and withering attacks from his fellow Republicans.

Romney's backing among Republican primary voters held steady at 23 percent. And Cain, buoyed by strong debate performances and media attention after he won a Florida Republican party straw poll, rose to third, just behind Perry at 17 percent, to join the top tier of candidates.

Among other contenders, the most dramatic shift in support was the decline of Michele Bachmann to just 3 percent backing. In late August, the Minnesota congresswoman had the backing of 8 percent of Republican primary voters, and her high was 15 percent in July.

Former House Speaker Newt Gingrich regained some ground to hit 11 percent and Texas Congressman Ron Paul is at 6 percent support, versus 8 percent before the September debates, according to the survey.

A majority of those surveyed -- 63 percent -- said they are happy with the current field of Republican candidates.

Among all voters, Democratic President Barack Obama still leads all the Republican hopefuls, topping Romney by 3 points and Perry by 8 points, Fox News said.

The telephone poll of 925 registered voters was conducted from September 25 to September 27. It has a margin of error of plus or minus 3 percentage points.

(Reporting by Patricia Zengerle, editing by Anthony Boadle)