Rarely in American politics has a leading presidential candidate made such grave accusations about a rival: warning that he is willing to violate the Constitution. Claiming that he is eager to persecute political rivals. Calling him a dire threat to democracy.

Those arguments have come from President Biden’s speeches, including his forceful address on Friday, as he hammers away at his predecessor. But they are also now being brazenly wielded by Donald J. Trump, the only president to try to overthrow an American election.

Three years after the former president’s supporters stormed the Capitol, Mr. Trump and his campaign are engaged in an audacious attempt to paint Mr. Biden as the true menace to the nation’s foundational underpinnings. Mr. Trump’s strategy aims to upend a world in which he has publicly called for suspending the Constitution, vowed to turn political opponents into legal targets and suggested that the nation’s top military general should be executed.

The result has been a salvo of recriminations from the top candidates in each party, including competing events to mark Saturday’s third anniversary of the attack on the Capitol.

The eagerness from each man to paint the other as an imminent threat signals that their potential rematch this year will be framed as nothing short of a cataclysmic battle for the future of democracy — even as Mr. Trump tries to twist the very idea to suit his own ends.

“Donald Trump’s campaign is about him — not America, not you,” Mr. Biden said Friday, speaking near Valley Forge in Pennsylvania. “Donald Trump’s campaign is obsessed with the past, not the future. He’s willing to sacrifice our democracy, put himself in power.”

On Friday evening, at his own rally in Sioux City, Iowa, Mr. Trump fired back, calling Mr. Biden’s remarks “pathetic fear-mongering” and again accusing him, without any evidence, of wielding federal law enforcement to attack his political opponents.

“They’ve weaponized government, and he’s saying I’m a threat to democracy,” Mr. Trump said incredulously.

The early maneuvering by Mr. Biden and Mr. Trump points to an election that will be fought on extraordinary ground. While the economy, abortion rights and the ages of the candidates are all expected to be central campaign issues, both men argue that what is fundamentally at stake is whether the country’s nearly 250-year-old system of government endures.

Mr. Biden traveled near the historical site — where George Washington burnished his leadership credentials during the Revolutionary War — to highlight the nation’s long tradition of a peaceful transfer of power, which Washington set in motion by voluntarily stepping down from office. The Biden campaign’s aim was to contrast that choice with the actions of Mr. Trump, who has continued to falsely dispute the results of the 2020 race.

The president’s team described the Friday speech as the first in a series of campaign events that would cast the coming election as a fight for the survival of democracy itself.

As Mr. Biden heads into the final year of his term, his worries that Mr. Trump could stoke more political violence have helped persuade him to make the strength of American democracy the fundamental question of his re-election, according to a longtime aide.

The stakes are especially personal for Mr. Trump given the 91 felony charges against him, many of them stemming from his attempt to cling to power. He often defines threats to democracy as any circumstance that could imperil his path to the presidency, and has assigned blame to Mr. Biden and his allies without evidence.

“They’re willing to violate the U.S. Constitution at levels never seen before in order to win,” Mr. Trump said during a rally last month in New Hampshire. “And remember this: Joe Biden is a threat to democracy — he’s a threat.”

In an email to supporters on Dec. 14, Mr. Trump falsely claimed that Jack Smith, the special counsel leading the federal prosecution of the former president, “was given one order from his boss — try, convict, and sentence Donald Trump to jail before the November 2024 election.”

Mr. Smith is responsible for investigating attempts to interfere with the 2020 election.

“You too could be jailed for life as an innocent man,” Mr. Trump warned supporters in a fund-raising appeal on Dec. 20.

In his attacks on Mr. Biden, the former president has often pointed to the moves by the Colorado Supreme Court and the Maine secretary of state to block Mr. Trump from the primary ballot in those states by citing a constitutional provision that prohibits those who “engaged in insurrection” from holding office.

Mr. Trump has correctly pointed out that Democrats have spearheaded such efforts to remove him from the ballot, but he rarely mentions that both decisions have been put on hold pending legal appeals — a sign of democratic institutions at work, not being undermined.

At campaign rallies, Mr. Trump has referred to the Jan. 6 attacks as “a beautiful day” and said the roughly 1,240 people arrested so far in connection with the riot were “hostages,” not prisoners. Nearly 900 have pleaded guilty or been convicted at trial.

A memo on Jan. 2 from Mr. Trump’s top campaign advisers, Chris LaCivita and Susie Wiles, made it clear that the former president’s strategy would define his election bid.

“Please make no mistake,” they wrote. “Joe Biden and his allies are a real and compelling threat to our democracy. In fact, in a way never seen before in our history, the are waging a war against it.”

Of course, Mr. Trump has often relied on projection as a political defense mechanism, including a memorable debate moment in 2016 when Hillary Clinton, the Democratic presidential nominee, said President Vladimir V. Putin of Russia had praised Mr. Trump because “he would rather have a puppet as president of the United States.”

“No puppet,” Mr. Trump quickly objected. “You’re the puppet.”

As president, Mr. Trump complained about the unruliness of House Democrats while leading a White House often consumed by chaos. He was impeached the first time after asking Volodymyr Zelensky, the president of Ukraine, to dig up dirt on Mr. Biden and his son — even as Mr. Trump accused the Biden family of unethical behavior in the Eastern European country.

More recently, Mr. Trump’s campaign has projected the words “BIDEN ATTACKS DEMOCRACY” onto screens at his rallies, and his team hands out matching signs to the crowd.

“It is classic Trump to try and deflect from his own misconduct,” Josh Shapiro, the Democratic governor of Pennsylvania, told reporters before Mr. Biden’s speech on Friday. “The reality is the people of Pennsylvania have shown through multiple cycles, in 2020 and 2022, that they see through that.”

Mr. Trump’s tactics have been adopted by supporters, including Representative Marjorie Taylor Greene of Georgia, who said this week that the Biden administration was “weaponizing the F.B.I. to go after MAGA grandmas and veterans” as she campaigned for Mr. Trump in Iowa.

“Democrats love democracy so much, they’re willing to destroy democracy in order to supposedly protect democracy,” Ms. Greene told a crowd in Keokuk on Thursday.

Polling has suggested that voters still prioritize issues like the economy over concerns about democracy. But Mr. Biden’s aides say their campaign data shows that his supporters are concerned about the risk of political violence and that Jan. 6 remains a resonant moment for the Democratic coalition.

While Democratic voters appear wary of Mr. Biden’s age and relatively unenthusiastic about his candidacy, they are firmly united by the idea that Mr. Trump has broken the public trust.

In a New York Times/Siena College poll last month, 93 percent of likely Democratic voters said they believed Mr. Trump had committed serious federal crimes. Eighty-seven percent of Democrats said Mr. Trump had been charged mostly because prosecutors believed he committed crimes — not because of political motivations.

Both figures outpaced the 79 percent of Democrats who said they approved of Mr. Biden’s performance as president.

Focusing on democracy “is the most salient way to capture the violence and extremism that MAGA represents,” said Navin Nayak, a Democratic strategist and the president of the Center for American Progress Action Fund. “It animates that the threat is still real and there is a future threat of violence.”

Republicans feel far differently. In the same survey, 69 percent of likely G.O.P. voters said Mr. Trump had not committed serious federal crimes and 84 percent said the charges were mostly motivated by politics.

“I think it’s all trumped up — they’re just doing it to spite him,” Terry Remillard, 62, said at Mr. Trump’s rally on Friday in Sioux Center, Iowa. “There’s no truth to any of those charges.”

One of the biggest questions for 2024 is whether moderate and independent voters in the general election buy the version of democracy that Mr. Trump is trying to sell them.

In 2022, the former president faced a resounding rejection from voters when he helped make his false election claims one of the top issues in the midterm elections. Losses by his handpicked candidates prevented Republicans from winning the Senate majority, Trump-backed candidates lost key races for governor in battleground states, and candidates he endorsed in competitive House races were defeated.

In the Times/Siena poll, majorities of likely independent voters said that Mr. Trump’s felony charges were not politically motivated, that the former president had committed serious federal crimes and that he had knowingly made false claims that the election was stolen.

Still, Mr. Biden’s lead against Mr. Trump among all likely voters — two percentage points — was well within the poll’s margin of error.

Reid J. Epstein contributed reporting from Blue Bell, Pa., and Kellen Browning from Sioux Center, Iowa.