Nothing in the Constitution gives President Trump the power to delay the November election, and even fellow Republicans dismissed it out of hand when he broached it on Thursday. But that was not the point. With a possible defeat looming, the point was to tell Americans that they should not trust their own democracy.

The idea of putting off the vote was the culmination of months of discrediting an election that polls suggest Mr. Trump is currently losing by a wide margin. He has repeatedly predicted “RIGGED ELECTIONS” and a “substantially fraudulent” vote and “the most corrupt election in the history of our country,” all based on false, unfounded or exaggerated claims.

It is the kind of language resonant of conspiracy theorists, cranks and defeated candidates, not an incumbent living in the White House. Never before has a sitting president of the United States sought to undermine public faith in the election system the way Mr. Trump has. He has refused to commit to respecting the results and, even after his election-delay trial balloon was panned by Republican allies, he raised the specter on Thursday evening of months of lawsuits challenging the outcome.

Mr. Trump has put on the line not merely the outcome of this fall’s contest but the credibility of the system as a whole, according to even scholars and operatives normally sympathetic to the president. Just floating the possibility of postponing a presidential election, an idea anathema in America and reminiscent of authoritarian countries without the rule of law, risks eroding the most important ingredient in a democracy — the belief by most Americans that, whatever its manifest flaws, the election result will be fundamentally fair.

“It undermines the faith of the public in our electoral process,” said Jonathan Turley, a George Washington University law professor who testified on Mr. Trump’s side last year during the House impeachment hearings. “Any constitutional system is ultimately held together by a leap of faith. Citizens must trust the process if you want them to yield to it. What the president is doing is seeding distrust about the legitimacy of even the holding of the election.”

Michael J. Gerhardt, a constitutional scholar at the University of North Carolina who testified on the other side in those hearings, said Mr. Trump’s statements were part of a pattern of disdain for the norms that have defined the United States for generations.

“In the long term, I think there’s going to be a lot of institutional damage,” he said, “and the rule of law is going to be undermined to a very large extent.”

Even some of Mr. Trump’s own current and former advisers see his attacks on the election system as a reflection of fear that he may lose and as a transparent effort to create a narrative to explain that away. Sam Nunberg, an adviser on Mr. Trump’s 2016 campaign, said the president was “trying to get ahead of a potential loss” by blaming it on external factors like the coronavirus.

“What President Trump does not seem to understand is that unlike past experiences where he was able to frame a defeat as a win, there is no spin for losing a re-election as an incumbent president and taking down the Republican Party with him,” Mr. Nunberg said. “Despite what he may believe, even the overwhelming majority of the president’s supporters are not interested in this claptrap.”

He added: “Republican voters and conservative media will ultimately feel that if you cannot beat Joe Biden, you do not deserve another term.”

As recently as April, a Republican National Committee official said former Vice President Joseph R. Biden Jr. was “off his rocker” to suggest that Mr. Trump might seek to “kick back the election somehow.” But in fact, Mr. Trump has a long history of sowing doubt in election results that do not go the way he wants them to go.

When he appeared to be losing to Hillary Clinton in 2016, he repeatedly suggested that the election was being rigged and would not commit to accepting the results — until he won, that is. And even after winning the Electoral College, he insisted that he had actually won the popular vote, too, because three million illegal immigrants had supposedly voted for Mrs. Clinton, a claim seemingly made up out of thin air and one for which his own commission found no evidence.

In 2020 alone, Mr. Trump has already made public comments, posted Twitter messages or reposted others suggesting election fraud 91 times, according to data compiled for The New Yorker by Factba.se, a service that collects and analyzes data on his presidency. Going back to 2012, Factba.se counted 713 instances when Mr. Trump cited vote fraud, spiking especially in 2016 and 2018 before elections in which he had a stake.

Some of Mr. Trump’s allies have said that he has justifiable reasons to raise concerns about widespread mail-in voting being employed in light of the coronavirus pandemic, even though there is a long history of its use without evidence of widespread fraud. And they accuse the Democrats of being the ones unwilling to accept election results when they lose, pointing to the yearslong effort to investigate Russian interference in the 2016 campaign and any ties to Mr. Trump’s organization.

In an interview last year with CBS News, Mrs. Clinton made clear that she considered Mr. Trump’s election shady. “I believe he knows he’s an illegitimate president,” she said.

She is hardly the only defeated candidate to see injustice in her loss. Going back to the early days of the republic, questions have been raised about the legitimacy of presidential victories from those on the losing side.

Andrew Jackson, who won the popular vote and had the most Electoral College votes in 1824 but not a majority in a four-way race, ended up losing to John Quincy Adams when the House decided the matter. Jackson spent the next four years accusing Adams of a making a “corrupt bargain” to secure the support of the third-place candidate, Henry Clay, in exchange for appointment as secretary of state. Jackson got his revenge by beating Adams in an 1828 rematch.

Likewise, Democrats complained when Rutherford B. Hayes won in a disputed election in 1876, calling him Rutherfraud B. Hayes and His Fraudulency. Republicans suspected that John F. Kennedy beat Richard M. Nixon in 1960 thanks to vote fraud in Texas and Illinois, and many Democrats never accepted George W. Bush’s victory over Al Gore in 2000 after the Florida recount was halted by the Supreme Court.

But the complaints do not typically come from the Oval Office, especially before an election has even been held. And no sitting president has made a serious effort to delay his own re-election, not even Abraham Lincoln in 1864 during the Civil War or Franklin D. Roosevelt in 1944 during World War II. Elections were held as scheduled during the pandemics of 1918 and 1968, as well.

Ronald C. White, a prominent Lincoln biographer, noted that the 16th president did not try to postpone the election even though he thought he was likely to lose. Instead, he made it possible for soldiers in the field to cast their ballots, recognizing that they might support their former general, George B. McClellan, who was his Democratic challenger.

“Even as the pandemic, economic collapse and racial protests have Trump calling himself a wartime president, the real wartime president, Lincoln, determined that the election of 1864 must go forward as a sign that the Union would go forward,” Mr. White said.

Jill Lepore, a Harvard University professor and the author of “These Truths: A History of the United States,” said presidents bear a responsibility to foster faith in democracy.

“Far from undermining public confidence in the democracy over which he presides, it is the obligation of every president to cultivate that confidence by guaranteeing voting rights, by condemning foreign interference in American political campaigns, by promoting free, safe and secure elections, and by abiding by their outcome,” she said.

Mr. Trump has for years been drawn to leaders of other countries who did not share that view, especially autocrats like Presidents Vladimir V. Putin of Russia, Recep Tayyip Erdogan of Turkey and Xi Jinping of China. He has expressed admiration for their leadership and envy that in their systems they can be decisive without bureaucratic or political impediments while avoiding criticism of their crackdowns on internal dissent.

For Americans who have made it their mission to encourage free and fair elections in countries like those and elsewhere, Mr. Trump’s suggestion to delay the November vote and his drumbeat of criticism leading up to it sounded like what they confront abroad, not at home

“I have never seen such an effort to sow distrust in our elections,” said Michael J. Abramowitz, the president of Freedom House, a nonpartisan organization that promotes democracy around the world. “We are used to seeing this kind of behavior from authoritarians around the globe, but it is particularly disturbing coming from the president of the United States.”