None of the charges are true.
But as eight states and the District of Columbia vote on Tuesday in the biggest Election Day since the coronavirus forced a pause in the primary calendar, it is clear that Mr. Trump’s message has sunk in deeply with Republicans, who have shunned mail ballots.
Republican officials and strategists warned that if a wide partisan gap over mail voting continues in November, Republicans could be at a disadvantage, an unintended repercussion of the president’s fear-mongering about mail ballots that could hurt his party’s chances, including his own.
In Pennsylvania, Iowa, Indiana and New Mexico, all states voting on Tuesday that broadly extended the option to vote by mail this year, a higher share of Democrats than Republicans have embraced mail-in ballots.
“If the Republicans aren’t playing the same game, if we’re saying we don’t believe in mail-in voting and are not going to advocate it,” said Lee Snover, the Republican chair of Northampton County in Pennsylvania, “we could be way behind.”
Seventy percent of the 1.5 million requests for mail ballots in Pennsylvania came from Democrats, ahead of a Primary Day now overshadowed by nationwide protests of police misconduct, which could keep voters away from polling places not already closed because of the pandemic.
The president’s baseless claims that mail voting leads to widespread fraud are working at cross-purposes to the state Republican Party’s efforts to increase mail voting.
“Democrats will use the new mail-in ballot to greatly increase their turnout,” the Republican Party of Pennsylvania says on its website. “Republicans would be smart to do the same so that we have the advantage.”
Pennsylvania will be one of the crucial battlegrounds in the presidential election, with parties doing all they can to turn out every supporter. Another county Republican chair, Giovanni Landi of Lehigh County, worried that the president was deterring the less consistent voters whose support he will need on Nov. 3.
“Republicans are constantly being warned that mail-in voting leads to vote fraud,” Mr. Landi said. “My concern is sometimes people think, ‘All right, I’m going to go to the polls,’ and then something comes up and they don’t make it to the polls.”
The same partisan divide is at work in other states voting on Tuesday that sent applications for mail ballots to all registered voters as a response to the coronavirus outbreak. In New Mexico, 71 percent of mail ballots returned as of Monday were from Democrats, according to the secretary of state. In Iowa, Democrats requested 56 percent of mail ballots, in a state where Democrats make up 50 percent of the voters registered by party.
In Indiana, which loosened its rules to offer no-excuse voting by mail, 350,000 Democrats requested mail ballots, compared with 268,000 Republicans, according to the secretary of state. Other states voting on Tuesday are Maryland, Montana, Rhode Island and South Dakota.
Iowa expects to have competitive races in the fall for a Senate seat and potentially for all four of its House seats. A Republican strategist who works for candidates in Iowa and other battleground states said if Mr. Trump continued his attacks on mail voting, it would significantly damage many of his clients in tough races.
To be sure, some partisan differences in mail voting trace to the electoral landscape of specific races. Some districts with competitive House primaries for Republicans but not for Democrats have had higher Republican participation. In Iowa’s Fourth District, where Representative Steve King, a vulnerable Republican, faces four primary challengers, Republican requests for mail ballots outpace those from Democrats.
Both parties expect record turnout nationwide in November. The most polarizing president of modern times seeks a second term. Majorities in both houses of Congress are in the balance. Voters with strong partisan views will most likely cast ballots by whatever means available, whether mailing them in, showing up at early-voting locations or turning out on Election Day.
It is the voters who don’t turn out like clockwork, many of whom have weak partisan identities, who can make a crucial difference in close-fought races. Those are the voters some Republicans fear will be lost to the party if mail voting is not embraced.
“The president has his viewpoint and we have ours; we’re trying to win elections,” said Dave Millage, the Republican chair of Scott County in Iowa. He anticipated that mail voting would also be popular in November, when Iowa Republicans will be defending a vulnerable senator, Joni Ernst, as well as trying to flip a congressional seat in the Second District, which includes Scott County.
“We will call everybody to request an absentee ballot and make sure they get them in,” Mr. Millage said. “You bank that vote, you don’t have to spend money to get them out to vote. You can cross them off the list.”
But so far, Mr. Trump’s disparagement of mail voting is winning out in Scott County, which encompasses Davenport. As of Monday, 10,344 Democrats had voted by mail, or 66 percent of the total, compared with 5,342 Republicans. Only 54 percent of county voters who are registered with a party are Democrats. Moreover, Republicans have a contested primary for the open House seat while Democrats do not.
Before Mr. Trump made mail voting toxic to many of his grass-roots supporters, it was widely used in many states, including some in which more Republicans than Democrats tended to vote absentee.
It was Republican majorities in the Pennsylvania Legislature that passed a bill last year expanding no-excuse mail voting to any registered voter. It was signed into law by Gov. Tom Wolf, a Democrat.
Mr. Trump, who has voted by mail in Florida, has weaponized the issue recently as polls showed him falling behind in battleground states. He falsely claimed a Democratic secretary of state in Michigan had “illegally” sent absentee ballot requests for the November election, and he threatened to hold back federal funds to Nevada if its Republican secretary of state went ahead with plans to send mail ballots directly to registered voters before its June 9 primary.
Last week, the president tweeted: “There is NO WAY (ZERO!) that Mail-In Ballots will be anything less than substantially fraudulent. Mail boxes will be robbed, ballots will be forged & even illegally printed out & fraudulently signed.”
The tweet led Twitter for the first time to add a disclaimer to one of Mr. Trump’s declarations, calling his claims of voter fraud “unsubstantiated.”
Although absentee voting is more susceptible to fraud than in-person voting, experts say that occurrences are rare and a scheme large enough to change the results of a statewide race would be easily detected.
At the same time, the rapid expansion of mail voting creates headaches for election officials who must authenticate and count a deluge of ballots, often delaying results beyond election night.
Five states, including Republican-leaning Utah, conduct nearly all elections exclusively by mail. There is no evidence that widespread use of mail voting benefits Democrats, as Mr. Trump fears.
In Arizona, where about 80 percent of voters cast early ballots, most by mail, in the 2018 midterms, a Republican governor, Doug Ducey, was re-elected while a Democrat, Kyrsten Sinema, won a Senate seat.
“We Arizonans look with some amusement upon the national debate raging around mail ballots,” said Kirk Adams, a former chief of staff to Mr. Ducey. “The majority of mail-in ballots requested are Republican ballots.”
Some Republicans dismissed concerns about fewer Republicans voting by mail this month, arguing they have good reason to be suspicious of the process.
On the Facebook pages of Republican parties in Pennsylvania, skepticism ran strong. “I would never trust mail in ballots!” wrote a voter named Elliott Stewart of Northampton County. “Get out and vote.”
A Bucks County voter, Diane Lisowski, wrote of mail voting: “NOT A GOOD IDEA!! I will be there in hazmat suit if i have to. Don’t trust the dems. They have shown over and over again, THEY ARE corrupt and WILL find a way to make it work in their favor!”
Other officials said that historically, Republicans simply have a preference for casting ballots in person on Election Day.
“Republicans intend on voting at their polling locations in June,” said Jim Christiana, the chair of the Beaver County G.O.P. in western Pennsylvania. “Hopefully, if things continue down the path as they have been lately, they’ll be voting at their polling locations in November as well.”