Sen. Elizabeth Warren has risen to the top of the 2020 Democratic presidential field in Iowa, with Sen. Kamala Harris and former Vice President Joseph R. Biden close behind, according to a survey released Wednesday.

Ms. Warren had the support of 20% of likely Democratic caucus-goers, followed by Ms. Harris at 18% and Mr. Biden at 17%, according to the David Binder Research poll conducted for the group Focus on Rural America.

Sen. Bernard Sanders was next at 12%, followed by South Bend, Indiana Mayor Pete Buttigieg at 10%, Sen. Amy Klobuchar at 4%, and Sen. Cory Booker at 2%. No other candidate topped 1%.

In March, Mr. Biden had led at 25%, followed by Mr. Sanders at 17%, Ms. Harris at 9%, Ms. Warren at 8%, and Mr. Booker at 7%. Mr. Buttigieg, Ms. Klobuchar, and former Rep. Beto O’Rourke had all been at 6%.

At 22% support, Ms. Harris led the way among respondents who said they watched all or some of the debates last week, and was followed by Ms. Warren at 20%.

Among those who didn’t watch but tracked coverage afterward, Ms. Warren led the way at 23%, followed by Mr. Biden at 17% and Ms. Harris at 15%.

Among people who didn’t watch and heard little to nothing about the debates, Mr. Biden led with 25% support, followed by Mr. Sanders at 20% and Ms. Warren at 15%.

The survey of 600 registered voters who said they were likely to participate in the 2020 caucuses was conducted from June 29-July 1 and has a margin of error of “no greater than” plus or minus 4%.

Mr. Binder, whose firm is based in San Francisco, conducted polling for President Obama in 2008 and 2012.

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