Former Vice President Joseph R. Biden holds a narrow edge in Iowa over Sen. Elizabeth Warren, and Mayor Pete Buttigieg of South Bend, Indiana, is now running in third place, according to a poll released Monday on the 2020 Democratic presidential field.

Mr. Biden was at 18% support, followed by Ms. Warren of Massachusetts at 17% and Mr. Buttigieg at 13%, according to the Suffolk University/USA Today poll.

Sen. Bernard Sanders of Vermont was at 9%, and 29% said they were undecided.

In a poll taken at the end of June, Mr. Biden had led Ms. Warren by double digits and Mr. Buttigieg was at 6% support.

“Iowa is unquestionably up for grabs,” said David Paleologos, director of the Suffolk Political Research Center. “[Buttigieg] has found a lane and is accelerating toward the front of the pack, surpassing Bernie Sanders. All of this is happening while the number of undecided voters continues to grow as Democratic caucusgoers pause to reevaluate the changing field.”

Among people who watched last week’s Democratic debate, Mr. Buttigieg led with 19% support, followed by Mr. Biden and Ms. Warren at 17% apiece.

About one in four respondents said Mr. Biden did worse than expected in the debate — tops in the field.

The survey of 500 likely Democratic caucus-goers was taken from Oct. 16-18 and has a margin of error of plus or minus 4.4 percentage points.

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