Former South Bend, Indiana, Mayor Pete Buttigieg has surged to the top of the 2020 Democratic presidential pack in New Hampshire, according to a poll released Thursday that shows former Vice President Joseph R. Biden, Sen. Bernard Sanders of Vermont and Sen. Elizabeth Warren of Massachusetts close behind.

Mr. Buttigieg was the top choice of 20% of voters likely to vote in the state’s Feb. 11 Democratic presidential primary, and was followed by Mr. Biden at 19%, Mr. Sanders at 18% and Ms. Warren at 15%, according to the Monmouth University poll, which described the contest as “effectively a four-way race right now.”

Compared to September, Mr. Buttigieg has picked up 10 points of support and Mr. Sanders, who won the 2016 New Hampshire primary, has gained 6 points.

Since then, Ms. Warren has lost 12 points of support and Mr. Biden has lost 6 points.

In the poll released Thursday, Sen. Amy Klobuchar of Minnesota was next at 6%, followed by Rep. Tulsi Gabbard of Hawaii and billionaire former hedge fund manager Tom Steyer at 4% apiece, tech entrepreneur Andrew Yang at 3%, Sen. Michael Bennet of Colorado at 2% and Sen. Cory A. Booker of New Jersey at 1%.

Former New York Mayor Michael Bloomberg, who didn’t file to get his name on the ballot, was not included in the poll.

“The race remains fairly wide-open. To the extent that New Hampshire voters could take some cues from Iowa, it’s also worth keeping an eye on lower polling candidates like Klobuchar if any of the leading contenders stumble in the earlier Iowa contest,” said Patrick Murray, director of the Monmouth University Polling Institute.

Ahead of a Friday deadline to qualify for next week’s debate, the survey did not help candidates like Mr. Booker, Mr. Steyer, and Mr. Yang who have met the Democratic National Committee’s fundraising requirements but still need to hit 5% support in at least two more qualifying polls.

Absent additional help, that would leave five candidates on the stage in Des Moines on Tuesday: Mr. Biden, Mr. Buttigieg, Ms. Klobuchar, Mr. Sanders, and Ms. Warren.

The survey of 404 likely Democratic primary voters was taken from Jan. 3-7 and has a margin of error of plus or minus 4.9 percentage points.

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