Former Vice President Joseph R. Biden leads his 2020 Democratic presidential rivals, but he has lost support since last month’s debate as Sen. Kamala D. Harris has improved her standing, according to polling released Tuesday.

Mr. Biden was the top choice of 31% of potential Democratic primary voters, followed by Sen. Bernard Sanders of Vermont at 19%, Ms. Harris of California at 14% and Sen. Elizabeth Warren of Massachusetts at 13%, according to the Morning Consult poll.

Pete Buttigieg, the mayor of South Bend, Indiana, was next at 6%, followed by former Rep. Beto O’Rourke of Texas at 3% and Sen. Cory A. Booker of New Jersey at 2%.

Support for Mr. Biden dropped 7 points compared to a survey in late June ahead of the first debate, while support for Ms. Harris increased by 8 points.

Among potential black Democratic primary voters, Mr. Biden was also still the first choice of 38% of respondents, followed by Mr. Sanders at 21% and Ms. Harris at 16%. But Mr. Biden’s support among that demographic declined by 8 points since late June, while Ms. Harris gained 7 points and Mr. Sanders gained 4 points.

Ms. Harris had confronted Mr. Biden at the debate about his past stance on federally mandated busing to desegregate schools, as well as his comments last month in which he talked up his past work with segregationist senators.

Mr. Biden has since defended his civil rights record and says he supported voluntary busing. After initially refusing to apologize for his comments about the segregationist senators, he did so over the weekend before a largely black audience in South Carolina.

The survey of 16,599 potential Democratic primary voters was taken from July 1-7 and has a margin of error of plus or minus 1%.

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