Jumping into the presidential campaign like no other two-term incumbent, President Obama warned Donald Trump on Tuesday to “stop whining” about a rigged election system, calling the Republican nominee’s claims “unprecedented” and false.

Speaking at a press conference in the dignified confines of the White House Rose Garden with the prime minister of Italy by his side, Mr. Obama couldn’t resist criticizing Mr. Trump in harsh terms, even after professing to be “subdued” because he wasn’t at a campaign rally.

“I’d invite Mr. Trump to stop whining and go try to make his case to get votes,” Mr. Obama said. “I have never seen, in my lifetime or in modern political history, any presidential candidate trying to discredit the elections and the election process before votes have even taken place. It’s unprecedented. It happens to be based on no facts.”

The president said Mr. Trump is trying to blame others for his impending loss on Election Day, and said the Republican’s whining proves “you don’t have what it takes to be in this job.”

Mr. Trump has accused the media of “rigging” the election in favor of Democrat Hillary Clinton, and has raised concerns about voter fraud. He repeated those claims Tuesday, pointing to a report by the Center for Public Integrity that said 96 percent of journalists who donated to a political campaign in this election cycle gave money to Mrs. Clinton.

“The media is an extension of the Clinton campaign, and they are trying to rig this election,” Mr. Trump said. “They even want to try and rig the election at the polling booths, where so many cities are corrupt and voter fraud is all too common.”

While the president sought to dismiss Mr. Trump’s claims of election rigging, Mr. Obama was careful to say only that there is no “significant” voter fraud in the U.S.

“Every expert, regardless of political party, regardless of ideology, conservative or liberal, who has ever examined these issues in a serious way, will tell you that instances of significant voter fraud are not to be found,” Mr. Obama said. “There is no evidence that that has happened in the past or that there are instances in which that will happen this time.”

There is evidence of voter fraud across the U.S., but not evidence that fraud occurs on a large scale.

The Heritage Foundation’s voter fraud database has documented more than 400 cases of proven voter fraud throughout the U.S., from examples of vote-buying, ineligible voting, false registrations and fraudulent use of absentee ballots.

In Minnesota, for example, there were more than 100 convictions for various voter fraud offenses from 2008 to 2011, including ineligible voting, false registrations and fraudulent use of absentee ballots.

And a study by the watchdog Public Interest Legal Foundation found that 1,046 ineligible noncitizens had successfully registered to vote in eight Virginia counties.

Conservatives assert that such examples most often benefit Democrats. Progressives, meanwhile, blame the right for long-running efforts at voter disenfranchisement, such as voter ID laws, to keep mostly low-income and minority citizens from voting — people who tend to vote for Democratic candidates.

The Brennan Center for Justice at the New York University School of Law found in a study that minorities, low-income and older citizens are less likely to have photo IDs, and that those groups are more likely to live long distances from ID-issuing offices.

Referring to reports that some Trump supporters are advocating violence against Mrs. Clinton if she wins, Mr. Obama said, “Democracy by definition works by consent, not by force.”

The president said voter fraud in the U.S. is virtually nonexistent, and that rigging elections is nearly impossible due to the “decentralized” nature of state and local election systems. Mr. Obama said he believes so deeply in the reliability of the election system that he will escort Mr. Trump to the U.S. Capitol for his swearing-in as president if the Republican receives more electoral votes on Election Day.

“It would be my expectation of Hillary Clinton to offer a gracious concession speech and pledge to work with him in order to make sure that the American people benefit from an effective government,” Mr. Obama said. “And it would be my job to welcome Mr. Trump, regardless of what he’s said about me or my differences with him on my opinions, and escort him over to the Capitol, in which there would be a peaceful transfer of power.

“That’s what Americans do. That’s why America is already great,” Mr. Obama added. “One way of weakening America, making it less great, is if you start betraying those basic American traditions that have been bipartisan, and have helped to hold together this democracy now for well over two centuries.”

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