Election officials in dozens of states representing both political parties said that there was no evidence that fraud or other irregularities played a role in the outcome of the presidential race, amounting to a forceful rebuke of President Donald Trump's portrait of a fraudulent election.

Over the last several days, the president, members of his administration, congressional Republicans and right wing allies have put forth the false claim that the election was stolen from Trump and have refused to accept results that showed Joe Biden as the winner.

But top election officials across the country said in interviews and statements that the process had been a remarkable success despite record turnout and the complications of a dangerous pandemic.

"There's a great human capacity for inventing things that aren't true about elections," said Frank LaRose, a Republican who serves as Ohio's secretary of state. "The conspiracy theories and rumors and all those things run rampant. For some reason, elections breed that type of mythology."

Steve Simon, a Democrat who is Minnesota's secretary of state, said: "I don't know of a single case where someone argued that a vote counted when it shouldn't have or didn't count when it should. There was no fraud."

"Kansas did not experience any widespread, systematic issues with voter fraud, intimidation, irregularities or voting problems," a spokeswoman for Scott Schwab, the Republican secretary of state in Kansas, said in an email Tuesday. "We are very pleased with how the election has gone up to this point."

The New York Times contacted the offices of the top election officials in every state on Monday and Tuesday to ask whether they suspected or had evidence of illegal voting. Officials in 45 states responded directly to The Times. For four of the remaining states, The Times spoke to other statewide officials or found public comments from secretaries of state; none reported any major voting issues.

Statewide officials in Texas did not respond to repeated inquiries. But a spokeswoman for the top elections official in Harris County, the largest county in Texas with a population greater than many states, said that there were only a few minor issues and that "we had a very seamless election." On Tuesday, the Republican lieutenant governor in Texas, Dan Patrick, announced on Tuesday a $1 million fund to reward reports of voter fraud.

Some states described small problems common to all elections, which they said they were addressing: a few instances of illegal or double voting, some technical glitches and some minor errors in math. Officials in all states are conducting their own review of the voting — a standard component of the certification process.

Perhaps none of the Trump campaign's claims received more attention than an allegation made over the weekend in Pennsylvania by Rudy Giuliani, the president's personal lawyer. On Saturday, Giuliani held a news conference in the parking lot of a Philadelphia landscaping company and claimed that the election in the city had been rife with fraud.

The office of the state's top law enforcement official said that there was no evidence to support Giuliani's claims, and that the election in the state was "fair and secure."

"Many of the claims against the commonwealth have already been dismissed, and repeating these false attacks is reckless," said Jacklin Rhoads, a spokeswoman for Josh Shapiro, a Democrat who is Pennsylvania's attorney general. "No active lawsuit even alleges, and no evidence presented so far has shown, widespread problems."

What emerged in The Times' reporting was how, beyond the president, Republicans in many states were engaged in a widespread effort to delegitimize the nation's voting system.

Some Republicans have even turned to lashing members of their own party who, in their eyes, did not show sufficient dedication to rooting out fraud. In Georgia, where Biden is leading, the two Republican senators from Georgia, Kelly Loeffler and David Perdue, both of whom are in a runoff to gain reelection, have called for the resignation of the Republican secretary of state, Brad Raffensperger. "The secretary of state has failed to deliver honest and transparent elections," the senators said in a statement.

In Washington, the losing Republican candidate for governor, Loren Culp, has disputed the Republican secretary of state's determination that the election there was free of fraud. The secretary of state, Kim Wyman, has in turn challenged Culp, trailing by 14 percentage points in the results, to produce evidence. "It's just throwing grass at the fence at this point," she said in an interview, "See what sticks."

Democrats have more frequently been the target of criticism. Last week, the Republican leadership of the Pennsylvania state legislature called on Kathy Boockvar, the Democratic secretary of state, to step down. In Wisconsin, the Republican speaker of the Assembly announced he would form committees to investigate voter fraud in the wake of Biden's narrow victory in the state, though there is no evidence of any. Republican lawmakers in Michigan on Saturday voted to issue subpoenas for documents in search of "election irregularities."

Indeed, Republicans in all three "blue wall" states have initiated "investigations" or called for audits — which is redundant given the certification work already underway. Democrats say this is simply a way to undermine confidence in the results.

On Monday, the Trump campaign accelerated their legal efforts, filing a lawsuit in the seven Pennsylvania counties where the president lost that claimed mail voting created an unfair, "two-tiered" system during the election — though the system is also in place in counties the president won. The campaign also announced plans to file another suit in Michigan.

The president has kept up a barrage of Twitter posts with false claims about improprieties in Nevada and Pennsylvania, predicting he'd prevail in Georgia, where he is behind, and said Wisconsin "needs a little time statutorily," though he offered no explanation for what he meant.

Nellie Gorbea, the Democratic secretary of state in Rhode Island, said the amount of attention on the election would make illegal voting extremely difficult. "It would be nearly impossible to do voter fraud in this election because of the number of people tuned in," she said.

Voting fraud in the United States is extremely rare. The irregularities that do occur are often inconsequential, isolated in nature, and unlikely to alter the outcome of an election. The most significant episode of election fraud over the past several years involved an alleged effort to manipulate ballots to benefit a Republican candidate for Congress in North Carolina, Mark Harris, in 2018. The scheme forced a new election and an operative who worked for Harris, L. McCrae Dowless, is under indictment. Harris was not charged with wrongdoing, and denied any role.

In the case of the 2020 election, Biden's margins in the blue wall states of Pennsylvania, Michigan and Wisconsin are all in the tens of thousands. Even in Georgia, where Biden leads by more than 11,000 votes, it would be hard to uncover enough voting irregularities to change who won.

"We have not seen any evidence of fraud or foul play in the actual administration of the election," said Jake Rollow, a spokesman for Jocelyn Benson, the Democratic secretary of state in Michigan. "What we have seen is that it was smooth, transparent, secure and accurate."

Still, Trump has been fixated on voter fraud since 2016, when he falsely claimed that vote stealing had cost him the popular vote, which he lost by roughly 3 million. In the election's aftermath, he formed a voting fraud commission that disbanded with no findings amid charges of secrecy, bias and overreach.

Trump's campaign against the election system this year has relied on either outright fabrication or gross exaggeration involving the sorts of small problems that typically come up in elections.

In Ohio, for instance, LaRose said that while it was not unusual to discover a handful of improprieties in a statewide election, systemic fraud has not happened.

"In the past, I've referred people to local prosecutors and the attorney general for noncitizens voting," he said. "It's like tens or dozens of people, not hundreds. There's no acceptable level of voter fraud and we take every one of those cases seriously."

Simon, the Minnesota secretary of state, said one precinct near Duluth had to correct its vote totals after a clerical error resulted in double counting of some ballots.

The tension over voting has been most palpable in Georgia. The Trump campaign and the two Republican senators have complained about transparency, which Raffensperger, the secretary of state, called "laughable."

"We were literally putting releases of results up at a minimum hourly," he said in a statement. "I and my office have been holding daily or twice-daily briefings for the press to walk them through all the numbers. So that particular charge is laughable."

He added that while there were likely small instances of fraud, he did not expect it to be significant enough to affect the outcome.

The absence of any major findings of fraud or irregularities, and the willingness of even Republican election officials to attest to smooth operations, have also undercut Trump's legal efforts.

In Michigan, the Trump campaign has sued, saying that their poll watchers were not given access to properly observe ballot counting in Detroit. But election officials in the city deny that, saying there were dozens of poll watchers from both campaigns inside the main counting center there.

Last week, a judge denied a Trump campaign bid to halt counting based on complaints about observers, dismissing key evidence as "vague" and as "hearsay."

The accusations of fraud from the president and his allies were noticeably absent from states where Trump and his fellow Republicans did well.

In South Carolina, for instance, the Republican incumbent, Sen. Lindsey Graham, won relatively easily over Jaime Harrison, despite the fact that polls showed a tight race there. The South Carolina Election Board chairman John W. Wells said late Monday, "I have not heard of any" substantive allegations of fraud in the state, though he added he would await a final determination in the certification and protest process.

Asked if Graham was concerned about results in his state, a spokesman said the senator has "discussed states where the margins are close" but invited South Carolina voters to step forward with any "evidence of fraud or irregularities."

Graham, a close ally of Trump, has taken up the president's cause. He asked the Department of Justice to investigate claims made in an affidavit the Trump campaign shared with him from a Postal Service worker in Erie, Pennsylvania. The worker made allegations of impropriety at the local Postal branch based largely on a conversation he said he overheard.

Late on Tuesday, the House Oversight Committee reported on Twitter that the worker recanted his story in discussions with the Poster Service's Office of Inspector General.

One of the secretaries of state who did not respond to requests for comment about the election in his state was Corey Stapleton of Montana, an outgoing Republican. But Stapleton did post a message implicitly addressing the president's ongoing fraud claims. "I have supported you, Mr. President," he wrote. "But that time is now over! Tip your hat, bite your lip, and congratulate @JoeBiden."