After a strong performance in her first Democratic presidential debate, Senator Kamala Harris of California saw a significant increase in support in three polls released this week, as she and the rest of the Democratic primary field cut into the lead that former Vice President Joseph R. Biden Jr. has enjoyed since entering the 2020 race.

The three polls of likely Democratic voters — two were national surveys, and one polled Iowa caucusgoers — all showed Ms. Harris leaping into second place in the days after last week’s debates. They also showed a dip in support for Mr. Biden, though more than one in five respondents still said he was their first choice to become the Democratic presidential nominee.

Taken together, the polls also continued a broader trend in which Senator Elizabeth Warren of Massachusetts has gained ground as Senator Bernie Sanders of Vermont has fallen back. Ms. Warren remained solidly in the top tier, finishing third in all three polls; Mr. Sanders, who led several polls before Mr. Biden entered the race, finished fourth in each of them. The differences between the two were within the margins of error and thus statistically insignificant.

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All three polls were conducted by phone within four days of the first round of Democratic debates last week. While Ms. Harris appeared to benefit the most from her performance, gains in polling for particular candidates immediately after debates are often temporary.