Nearly one in five voters in battleground states says that President Biden is responsible for ending the constitutional right to abortion, a new poll found, despite the fact that he supports abortion rights and that his opponent Donald J. Trump appointed three Supreme Court justices who made it possible to overturn Roe v. Wade.

Trump supporters and voters with less education were most likely to attribute responsibility for abortion bans to Mr. Biden, but the misperception existed across demographic groups. Twelve percent of Democrats hold Mr. Biden responsible, according to New York Times/Siena College polls in Arizona, Georgia, Michigan, Nevada and Wisconsin and a Times/Philadelphia Inquirer/Siena poll in Pennsylvania.

“I think the buck stops with him, so he had the ability to fight that, and that’s not what I’m hearing that he did,” said Terri Yonemura, 62, an abortion rights supporter in Las Vegas who said she would not vote for Mr. Trump, but is unsure about Mr. Biden, so may not vote at all.

Abortion has been a mobilizing issue for Democrats in recent elections, and the confusion among a segment of voters presents both a challenge and an opportunity for Mr. Biden, who trailed Mr. Trump by six points in the survey overall.

“This group is a pickup opportunity for Democrats,” said Celinda Lake, a Democratic pollster who regularly surveys voters about abortion. The bigger challenge, she said, is that many voters do not understand Mr. Trump’s stance on the issue. “He has intentionally kept it vague. But when we show voters his statements in his own words, that is enough to persuade them.”