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Widespread concerns about President Biden’s age pose a deepening threat to his re-election bid, with a majority of voters who supported him in 2020 now saying he is too old to lead the country effectively, according to a new poll by The New York Times and Siena College.

The survey pointed to a fundamental shift in how voters who backed Mr. Biden four years ago have come to see him. A striking 61 percent said they thought he was “just too old” to be an effective president.

A sizable share was even more worried: Nineteen percent of those who voted for Mr. Biden in 2020, and 13 percent of those who said they would back him in November, said the 81-year-old president’s age was such a problem that he was no longer capable of handling the job.

The misgivings about Mr. Biden’s age cut across generations, gender, race and education, underscoring the president’s failure to dispel both concerns within his own party and Republican attacks painting him as senile. Seventy-three percent of all registered voters said he was too old to be effective, and 45 percent expressed a belief that he could not do the job.

This unease, which has long surfaced in polls and in quiet conversations with Democratic officials, appears to be growing as Mr. Biden moves toward formally capturing his party’s nomination. The poll was conducted more than two weeks after scrutiny of his age intensified in early February, when a special counsel described him in a report as a “well-meaning, elderly man with a poor memory” and “diminished faculties in advancing age.”

Previous polling suggests that voters’ reservations about Mr. Biden’s age have grown over time. In six top battleground states surveyed in October, 55 percent of those who voted for him in 2020 said they believed he was too old to be an effective president, a sharp increase from the 16 percent of Democrats who shared that concern in a slightly different set of swing states in 2020.