Mr. Trumpâs words, though, appear to be having an effect on his supporters, and are setting off deep concern among civil rights groups. According to an Associated Press last month, only one-third of Republicans said they had a great deal of confidence their votes would be counted fairly. And election officials are worried that Mr. Trumpâs continued pressing of the issue could dampen turnout or cause his supporters to deny the legitimacy of the results if he loses.
Last week, Mr. Trump called the presidential election âone big fixâ and âone big ugly lie.â
Jon A. Husted, the secretary of state of Ohio, said it was âwrong and engaging in irresponsible rhetoricâ for any candidate to question the integrity of elections without evidence. Mr. Husted, a Republican, said he would have no reason to hesitate to certify the results of the election
âWe have made it easy to vote and hard to cheat,â Mr. Husted said in an interview on Sunday. âWe are going to run a good, clean election in Ohio, like we always do.â
American elections are, unlike those in many democracies, largely decentralized, rendering the possibility of large-scale fraud extraordinarily unlikely. Further, the balloting in many of the hardest fought states will be overseen by Republican officials, individuals who would be highly unlikely to consent to helping Mrs. Clinton rig the vote.
Chris Ashby, a Republican election lawyer, said Mr. Trumpâs attacks on the electoral process were unprecedented and risked creating a fiasco on Election Day. Mr. Ashby also said the Mr. Trump was âdestabilizingâ the election by encouraging his supporters to deputize themselves as amateur poll monitors.
âThatâs going to create a disturbance and, played out in polling places across the country, it has the potential to destabilize the election,â Mr. Ashby said, âwhich is very, very dangerous.â
Mr. Trumpâs claims, a little more than three weeks before the election, are once again forcing elected Republicans into a difficult spot as they try to balance offering assurances of the integrity of the election while not undercutting a standard-bearer many of their voters fervently support.
âOur secretary of state, Ken Detzner, has been very focused on making sure we have a smooth election,â said Jackie Shutz, a spokeswoman for Gov. Rick Scott of Florida, noting that Mr. Scottâs âgoal is 100 hundred percent participation and zero percent fraud.â
Representatives of other Republican governors offered only a terse âyesâ when asked if their stateâs balloting would be conducted fairly.
Yet other Republicans are appalled at Mr. Trumpâs claims of widespread fraud, which are now a staple of his stump speech.
âIt is so irresponsible because what heâs doing really goes to the heart of our democracy,â said Trey Grayson, a Republican and former secretary of state of Kentucky. âWhat is great about America is that we change our leaders at the ballot box, not by bullets,â Mr. Grayson said.
Still, some of Mr. Trumpâs loyal backers are rousing one another with talk of insurrection should Mr. Trump be defeated.
In Wisconsin, David Clarke Jr., the sheriff of Milwaukee County, posted on Twitter on Saturday that it was, âPitchforks and torches time,â along with a photograph of an angry mob wielding weapons. Mr. Clarke addressed the Republican convention in July and appears regularly on television as a Trump campaign surrogate.
Also, elements of Mr. Trumpâs crowds have turned violent. At a rally in North Carolina on Friday, in which he alleged a large-scale conspiracy against him, one supporter lashed out physically at a protester in the crowd. And a CBS affiliate in Virginia reported over the weekend that pro-Trump demonstrators had flashed firearms outside the office of a Democratic congressional candidate near Charlottesville, in a threatening signal.
Republicans are also facing signs of menace: A party office in North Carolina was set on fire and spray-painted over the weekend, an act Mr. Trump wrote on Twitter was the act of âAnimals representing Hillary Clinton and Dems in North Carolina.â
Still, Mr. Trumpâs campaign surrogates have not hesitated to join him in questioning the fairness of the electoral process: Newt Gingrich, a former speaker of the House, and former Mayor Rudolph W. Giuliani of New York, both advisers to Mr. Trump, used television interviews on Sunday to suggest that Democrats tend to cheat in elections, accusing them of counting votes from dead people.
And Senator Jeff Sessions of Alabama, Mr. Trumpâs closest congressional supporter and a member of the Senate Judiciary Committee, has warned âthey are attempting to rig this election.â
Civil rights groups have begun to express alarm at remarks from Mr. Trump that they see as goading his supporters to intimidate minorities at the polls.
Arturo Vargas, the executive director of the National Association of Latino Elected Officials Education Fund, said he planned to formally contact the Justice Department as soon as this week, to ask that it guard against the kind of voting disruptions Mr. Trump has encouraged.
âIt is a major concern that we have this candidate promoting vigilante poll watching,â Mr. Vargas said.
And Michael Podhorzer, the political director of the A.F.L.-C.I.O., said that progressive groups were deeply concerned about the possibility of disruptions at the polls on Election Day. Mr. Podhorzer said that Mr. Trumpâs recent comments about a ârigged electionâ had the potential to âincite violence and bloodshed.â
Mr. Podhorzer said that Democrats would be closely monitoring polling places in states where voters can cast their ballots in advance of Election Day, to watch for signs of interference.
âWe will start to see whether folks are out intimidating voters in predominantly African-American communities, and at least get a sense of what direction that might be going in,â Mr. Podhorzer said, adding of Mr. Trumpâs rhetoric, âThis is beyond the pale.â
Other Democrats were just as bothered, but also amused about the unlikely prospect of a vast fraud plot unfolding at thousands of disparate polling places. âHeâs fine with the system when he wins the primary, but now heâs pre-emptively claiming precinct-level fraud?â said Lt. Gov. Gavin Newsom of California, calling Mr. Trumpâs language âunambiguously racist, but also absurd, ludicrous, and pathetic.â
Even House Speaker Paul D. Ryan, who just last week all but removed himself from the presidential campaign, was forced to issue a statement. âOur democracy relies on confidence in election results, and the speaker is fully confident the states will carry out this election with integrity,â said Mr. Ryanâs spokeswoman, AshLee Strong.
Mr. Pence is trying to walk a fine line. The governor, in a series of Sunday television interviews, sought to portray Mr. Trumpâs criticism of the electoral process as relating entirely to what he described as unfair news media coverage.