Even as other surveys show him slipping in some early states, former Vice President Joseph R. Biden holds a sizable advantage over the rest of the 2020 Democratic presidential field in South Carolina, home of the first-in-the-south primary, according to a CNN poll released on Sunday.

Mr. Biden was the top choice of 37% of likely Democratic primary voters in the state, followed by Sen. Elizabeth Warren of Massachusetts at 16% and Sen. Bernard Sanders of Vermont at 11%, according to the poll.

Mayor Pete Buttigieg of South Bend, Indiana, was next at 4%, followed by Sen. Kamala D. Harris of California and billionaire environmental activist Tom Steyer at 3% apiece.

Sen. Cory A. Booker of New Jersey and former Rep Beto O’Rourke of Texas were both at 2%, and no other candidate topped 1%.

Mr. Biden maintained his strength among black voters, a key constituency in the South Carolina primary, winning 45% support compared to 13% for Mr. Sanders, 6% for Ms. Harris, 5% for Mr. Steyer and 4% for Ms. Warren.

Six in 10 voters said it’s more important to them personally that the Democratic party nominate a presidential candidate with a strong chance of beating President Trump, compared to 27% who said it’s more important that the party nominate a candidate who shares their position on major issues.

The survey of 406 likely Democratic primary voters was taken from Sept. 22-26 and has a margin of error of plus or minus 5.9 percentage points.

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