Just two weeks after announcing his intention to seek a second term next year, President Biden’s poll numbers have sunk to the lowest yet of his presidency and even his fellow Democrats say they would prefer the party nominate someone other than the president as their candidate.

A new Washington Post-ABC poll out Sunday suggests that Mr. Biden’s approval rating is now down to 36 percent, a decline of six points since February. Nearly half of respondents, or 47 percent, said they disapprove “strongly” of the president’s performance.

Mr. Biden’s approval rating is underwater with many of the key constituent groups that supported him three years ago. Only a quarter of Americans under age 30, 42 percent of non-white voters, and 41 percent of urban residents told pollsters that they support the president.

Black voters formed the heart of Mr. Biden’s base of support and any dip in support could prove consequential in some of the most fiercely competitive states, such as Georgia, Michigan and Wisconsin.

After a dismal start to his 2020 presidential campaign, Black voters in South Carolina rallied behind Mr. Biden, reviving his White House ambitions by driving his Democratic rivals from the race and ultimately putting him on a path to defeating President Trump.

At the outset of Biden’s reelection bid, however, the conflicting views among the same voters provide an early warning sign of the challenges he faces as he aims to revive the diverse coalition that proved so crucial to him before.

Well aware of the challenge, the Biden campaign says it’s confident in its message and is planning to highlight how the president has prioritized issues that are important to Black Americans. Mr. Biden is scheduled to give a commencement address at Howard University, a historically black university in Washington, later this month.

“The progress made in the first two years — whether it’s the historically low black unemployment rate, unprecedented funding to HBCUs, or halving the black poverty rate in half — is all at stake in 2024,” a campaign spokesman, Kevin Munoz, told the Associated Press. “The campaign will work hard to earn every vote, and expand on its winning 2020 coalition.”

Yet there are some early signs that Biden will have work to do to generate enthusiasm among Black voters for another run.

Biden’s approval rating among Black adults has fluctuated over his two years in office. As with most demographic groups, the latest Associated Press-NORC Center for Public Affairs Research poll finds his 58 percent current approval rating among Black adults sitting well below where he began. Roughly 9 in 10 Black adults approved of Mr. Biden over his first months in office.

While only about half of Democrats overall say they want Biden to run again in 2024, 81 percent say they would definitely or probably support him if he were the nominee. The groundswell isn’t as stark among Black adults: 41 percent say they want him to run and only 55 percent say they are likely to support him in the general election, according to the AP poll.

Among younger voters, many say they aren’t convinced that Mr. Biden has delivered on their most important priorities. Many also cited the economy in the AP poll, especially lowering inflation, as a top priority. Several noted a lack of enthusiasm among their peers for a second Biden run, even while acknowledging they didn’t see a realistic alternative. But they wondered how lackluster support might affect turnout next year.

“For people to vote, and to be eager to vote, you have to actually want to vote for the person,” said Ace Conyers, a 22-year-old at South Carolina State.

A 22-year-old senior at South Carolina State University, Destiny Humphreys, echoed those sentiments in an interview with the Associated Press. “Honestly, I feel like right now America is in a state of emergency. We need some real change,” Ms. Humphreys said.

In the Washington Post-ABC poll, Mr. Trump leads among the expected Republican candidates, with twice as much support as the governor of Florida, Ron DeSantis. Asked who they would support in 2024, 44 percent of voting-age adults say they would “definitely” or “probably” vote for Mr. Trump while 38 percent would definitely or probably vote for Mr. Biden. The remaining 18 percent are either undecided or gave another answer.