Mr. Biden formally launched his re-election campaign with a video announcement Tuesday, a long-awaited declaration that puts him on the path to a potential rematch with the man he beat in 2020 and whom he accuses of endangering U.S. democracy—former President Donald Trump. The 2024 campaign will play out in an era of political polarization, with both parties fighting over a small number of battleground states and the narrow slice of the electorate that isn’t firmly in one camp or the other.

In the video, Mr. Biden frames the election as a question of “whether in the years ahead we have more freedom or less freedom, more rights or fewer. I know what I want the answer to be and I think you do, too. This is not a time to be complacent. That’s why I’m running for re-election."

The three-minute video opens with images of the Jan. 6, 2021, attack on the U.S. Capitol, and then references the Supreme Court’s overturning of Roe vs. Wade before Mr. Biden says the word: “Freedom," pointing to the American value as the key to his first term. Vice President Kamala Harris features prominently in the video, which warns against “MAGA extremists."

Already the oldest president in American history at 80 years old, Mr. Biden would be 86 at the end of a second term. A majority of Americans don’t approve of his performance as president and polls show ample public concern, even among many Democrats, about his age and fitness for office. Mr. Biden has answered questions about his age by saying that people should watch him do the job, and aides argue that his legislative record—including securing funding for the Covid-19 pandemic, and passing broad infrastructure and climate measures—will resonate with voters.

“Every generation of Americans has faced a moment when they’ve had to defend democracy, stand up for our personal freedoms, stand up for our right to vote and our civil rights. And this is our moment," Mr. Biden said in the video, urging supporters to visit his campaign website. “Let’s finish this job, I know we can."

The video kicked off Mr. Biden’s re-election campaign. The president plans to address the North America’s Building Trades Unions later in the day, allowing him to highlight his $1 trillion bipartisan infrastructure law. Ms. Harris will speak at a rally on abortion rights later in the day at Howard University, her alma mater.

Mr. Trump attacked Mr. Biden over high inflation and his handling of the southern border, while repeating his false claims that he won the 2020 election. “There has never been a greater contrast between two successive administrations in all of American history. Ours being greatness, and theirs being failure," he said.

The 2024 race, which will also determine the House and Senate majorities, will unfold very differently than in 2020, when candidates like Mr. Biden eschewed in-person campaigning. This contest will be much more heavily focused on abortion, as the 2022 midterm elections were. Mr. Biden has pledged to protect abortion access, while many Republican candidates support restrictions.

The president faces headwinds as he enters the race. According to a new Wall Street Journal poll, 42% of voters approve of the job Mr. Biden is doing, compared with 56% who disapprove, numbers that haven’t moved much in over a year. The poll also found that 15% of voters think the country is on the right track, and it showed Mr. Biden underwater with voters on nearly all major issues, including his handling of the economy and infrastructure.

Republicans have blamed Mr. Biden for high inflation. They also have criticized him over the chaotic withdrawal of U.S. forces from Afghanistan. Republican National Committee Chairwoman Ronna McDaniel said that Mr. Biden has created “crisis after crisis."

With the first primaries still months away, Mr. Trump is currently leading the Republican field, as he seeks to win another term after losing to Mr. Biden in 2020. The poll shows that in a direct contest with Mr. Trump, Mr. Biden gets 48% and Mr. Trump 45%. Against Florida Gov. Ron DeSantis, a Republican who is viewed as likely to launch his campaign in May or June, Mr. Biden gets 45% and Mr. DeSantis 48%. Mr. DeSantis is pictured briefly in Mr. Biden’s announcement video, standing next to Mr. Trump.

Mr. Biden and his advisers had considered formally launching his re-election bid toward the beginning of the year, as early as mid-February, but saw little urgency as Mr. Trump’s campaign struggled and the GOP field was slow to materialize. His team started scripting his campaign video before he traveled to Ireland earlier in April and filming began when he returned to Delaware.

The president faces two long-shot primary challengers in author Marianne Williamson and environmental lawyer Robert F. Kennedy Jr., the son of Robert F. Kennedy and nephew of former President John F. Kennedy. Democrats’ strong showing in the 2022 midterm elections, in which the party maintained control of the Senate, and a desire to avoid a divisive intraparty battle dissuaded any prominent Democrats from challenging Mr. Biden for the nomination.

Tuesday’s video reveal matches the low-key, Rose Garden strategy that Mr. Biden’s campaign will take for now. He is expected to keep his focus on being president, traveling and working in his official capacity, with some fundraising added to his schedule. The approach harks back to the re-election bid from former President Barack Obama, who announced his campaign launch in a video in April 2011, but didn’t hold his first official rally for his re-election until May 2012.

During his State of the Union address, Mr. Biden stressed the need to “finish the job," emphasizing climate change, child care for workers and raising taxes on the wealthy.

As Election Day draws closer, Mr. Biden is expected to conduct his campaign differently than in 2020. As a result of the once-in-a-century pandemic, Mr. Biden spent weeks holed up in his home after securing the nomination and then held a limited number of in-person events and rallies. But with the pandemic waning, he would be expected to have a more robust campaign presence this time.

Mr. Biden began his political career in local government in Delaware and then was elected to the Senate shortly before his 30th birthday. After more than three decades in the Senate, he served two terms as vice president to Mr. Obama, and then won the presidency in 2020. In office, he has overseen legislation to combat the Covid-19 pandemic, invest in the nation’s aging infrastructure and boost domestic manufacturing.

He has also pushed for—but so far has been unable to deliver—voting-rights legislation, a national paid-leave program, support for child care, changes to the immigration system and efforts to provide free community college.

Mr. Biden’s announcement allows his re-election campaign to begin fundraising and build out a staff, which will work in close partnership with the White House. Mr. Biden will also have a built-in infrastructure from the Democratic National Committee, which will play a key role in organizing supporters in battleground states. The DNC currently has $28.6 million in the bank, according to their latest financial statement.

The campaign is expected to be based in the president’s hometown of Wilmington, Del. Mr. Biden named Julie Chavez Rodriguez as his campaign manager Tuesday. Ms. Chavez Rodriguez is a White House senior adviser and the granddaughter of the late labor leader Cesar Chavez, whose bust is featured in Mr. Biden’s Oval Office. Quentin Fulks, who managed Sen. Raphael Warnock’s (D., Ga.) campaign, will serve as principal deputy campaign manager.

Top advisers Jennifer O’Malley Dillon, who managed the 2020 campaign, and Anita Dunn, who was the campaign’s senior adviser, are expected to help lead the effort from the White House.

Mr. Biden’s allies are gearing up in other ways. Top donors to Mr. Biden’s 2020 campaign and the DNC, including those who raised roughly $1 million or more, have been invited to meetings with Biden advisers in Washington next week.

The meetings are expected to include a gathering with Mr. Biden, according to people familiar with the plans.

The DNC held a similar event earlier in the month in Scottsdale, Ariz., which included a briefing with pollster David Binder; a presentation about lessons learned in top battleground states such as Georgia, Nevada and Wisconsin; and a session on the Republican presidential field, according to a copy of the agenda reviewed by the Journal.