 -- With just 21 days to go before Election Day, Donald Trump has claimed repeatedly on the campaign trail that the election is being “rigged,” tweeting on Monday that “large scale voter fraud” is a problem.

ABC News reached out to the top election official in each state to ask about Trump’s claim. Of the 26 officials who immediately responded, all maintained that the presidential election has not and will not be rigged in their state.

Manipulating Election Results Is Difficult, Officials Say

Washington Secretary of State Kim Wyman, a Republican, told ABC News that she “categorically disagree[s]” with Trump’s contention.

“I have spent the last 24 years of my professional career working in the field of elections and election administration, and I think that remarks like that made by any candidate are irresponsible because it really starts to undermine people’s confidence in the election process,” she said.

General elections are primarily run at the state and local levels, making a coordinated attempt to manipulate the results particularly difficult, officials say. In the 40 states where elections are overseen by a secretary of state or lieutenant governor, 25 of those top officials are Republican (including swing states Colorado, Florida, Iowa, Michigan and Nevada), and 15 are Democrats, according to Election Line.

Election officials who spoke to ABC News highlighted the benefits of a decentralized voting system. For example, in Texas, elections are conducted by counties, not the state.

“Texas has 254 counties using a variety of voting methods. The decentralized system in addition to layers of checks would make changing the outcome of a statewide election essentially impossible,” said Texas Secretary of State Carlos Cascos.

And in Vermont, where voting is also run at a local level, “someone trying to influence or change an election would have to hack into each town’s vote tabulators,” Vermont Secretary of State Jim Condos told ABC News.

There were a few attempts to hack or breach the voting system in Washington state, according to Wyman, but she told ABC News that the state’s security measures and firewalls held up and that no damage was done.

Officials Say Voter Fraud Is Rare

Election officials in 26 states told ABC News that they do not expect widespread voter fraud, citing only occasional or isolated cases. In the 10 states where election officials gave ABC News specific data on known voter fraud during the 2008 and 2012 presidential elections, only 18 cases were identified out of the millions of ballots cast.

Missouri: “Missouri did not have a single case of voter impersonation fraud” in the 2008 and 2012 presidential races. 2,925,205 and 2,757,323 ballots cast in 2008 and 2012, respectively, according to Stephanie Fleming, a spokeswoman for the Missouri secretary of state.

New York: “I am not aware of any individual prosecutions for voter fraud during either election,” said John Conklin, a spokesman for the New York Board of Elections. 7,722,019 and 7,135,322 ballots cast in 2008 and 2012, respectively.

Delaware: No voter fraud out of 826,302 votes cast, according to a Delaware Department of Elections spokeswoman.

New Mexico: One person indicted for requesting absentee ballots for a deceased voter, according to a spokesman for the New Mexico secretary of state. 833,365 and 786,522 ballots cast in 2008 and 2012, respectively.

Louisiana: Fewer than five incidents of voter fraud, according to a spokeswoman for the Louisiana secretary of state. 1,960,761 and 1,994,065 ballots cast in 2008 and 2012, respectively.

Massachusetts: No incidents of voter fraud, according to a spokesman for the Massachusetts secretary of the commonwealth. 3,102,995 and 3,184,196 ballots cast in 2008 and 2012, respectively.

Oregon: One voter fraud prosecution out of 1.8 million ballots cast in 2008 and 2012 combined, according to a spokeswoman for the Oregon secretary of state.

Rhode Island: No voter fraud, according to a spokeswoman for the Rhode Island secretary of state. 475,428 and 450,030 ballots cast in 2008 and 2012, respectively.

Oklahoma: No more than a dozen potential voter fraud incidents. “I am not aware of any that resulted in prosecution,” said Oklahoma State Election Board spokesman Bryan Dean. 1.46 million and 1.33 million votes cast in 2008 and 2012, respectively.

Washington: No voter fraud detected out of 6 million votes cast in 2008 and 2012 combined, said a spokesman for the Washington secretary of state.

A study by professor Justin Levitt of Loyola Law School found only 31 credible incidents of voter fraud out of approximately 1 billion ballots cast in general, primary, special and municipal elections nationwide from 2000 through 2014.

But critics say voter fraud is much more prevalent than that and goes largely undetected. The Public Interest Legal Foundation, for example, says that just in Pennsylvania and Virginia, thousands of noncitizens are illegally registered to vote and may likely commit election fraud.

Officials Admit That Election Problems Persist

While the election officials reached by ABC News are confident that the election results will reflect the will of the people, some conceded that voting problems exist.

In New York, for example, the State Enforcement Counsel is investigating allegations of election fraud, absentee fraud and New York City ID fraud.

During the 2013 mayoral election, the New York City Department of Investigation sent 63 undercover investigators to poll sites with the intention of impersonating voters, and 61 of them were allowed to vote, according to Conklin. “I believe this report demonstrated that someone with a little knowledge of how the system works can exploit it,” he said.

ABC News’ Mary Kathryn Burke, Teri Whitcraft, John Kruzel, Jack Date and James King contributed to this report.