With concerns mounting over how the country can conduct elections during a pandemic and Democrats pressing for alternatives to in-person voting, President Trump has begun pushing a false argument that has circulated among conservatives for years — that voting by mail is a recipe for fraud.

“Mail ballots, they cheat,” Mr. Trump said at the White House on Tuesday afternoon. “Mail ballots are very dangerous for this country because of cheaters. They go collect them. They are fraudulent in many cases. They have to vote. They should have voter ID, by the way.”

The president spoke as Wisconsin voters, many wearing protective masks, were going to the polls on a fraught Election Day, after the Republican-led legislature refused Democratic demands to delay the election and allow for expanded mail-in voting. On Wednesday, Mr. Trump claimed again that there was “tremendous potential for voter fraud.”

Here’s a look at the facts on the matter.

All voter fraud is extremely rare.

Studies have shown that all forms of voting fraud are extremely rare in the United States. A national study in 2016 found few credible allegations of fraudulent voting. A panel that Mr. Trump charged with investigating election corruption found no real evidence of fraud before he disbanded it in 2018.