All told, 50 percent of voters said they would vote for Mr. Biden in a head-to-head matchup, and 41 percent said they would vote for Mr. Trump. In an Monmouth poll in April, Mr. Biden led the president by just four percentage points; in March, he led by three. The margin of error in the new poll was plus or minus 3.6 percentage points.
A large majority of voters — 86 percent — were aware of the allegation that Mr. Biden sexually assaulted a Senate aide, Tara Reade, in 1993. Ms. Reade says he pinned her to a wall, reached under her clothing and penetrated her with his fingers.
After Mr. Biden publicly denied Ms. Reade’s accusation on Friday, Monmouth added a question to the poll already in progress, asking whether voters had heard about the allegation and whether they thought it was true.
Thirty-seven percent said it was probably true, 32 percent said it was probably not true, and 31 percent had no opinion. The margin of error for questions related to the assault allegation was plus or minus 4.1 percentage points.
There was a large partisan divide in whether voters viewed the allegation as credible. Republicans tended to say it was probably true, 50 percent to 17 percent, while Democrats tended to say it was probably not true, 55 percent to 20 percent. By two-to-one, independent voters were more likely to say it was true (43 percent) than to say it wasn’t (22 percent).
Among voters who said they believed the allegation, 59 percent supported Mr. Trump and 32 percent supported Mr. Biden. Among voters who did not believe the allegation, 79 percent supported Mr. Biden and just 14 percent supported Mr. Trump.
Mr. Biden was still seen more favorably overall than Mr. Trump: 41 percent of voters saw him favorably, while 44 percent saw him unfavorably. The president was seen positively by just 40 percent of voters, and negatively by 53 percent.
In a hypothetical three-way race with Justin Amash, a candidate for the Libertarian nomination, Mr. Biden still led Mr. Trump on the ballot — but by seven points, not by nine. Mr. Amash, an independent congressman from Michigan, about whom 81 percent of voters still said they had no opinion, earned 5 percent in that matchup, including 10 percent of independents.