Voting officials in both parties and academics across the country have long rejected the notion that fraudulent voting is widespread, finding instead that it is a sporadic and uncommon occurrence that has had no discernible effect on election outcomes. Mr. Trump’s own lawyers concluded as much about the 2016 contest, asserting in legal filings that it was “not tainted” as they sought to block recounts in Michigan, Pennsylvania and Wisconsin.

“There are problems in the registration system that don’t translate into fraud, there are sporadic and very rare instances of fraud, and voter impersonation fraud is the rarest of all,” said Nathaniel Persily, a professor of political science at Stanford who served as the research director of the bipartisan Presidential Commission on Election Administration in 2012.

“The notion that there is widespread voting by undocumented immigrants or other ineligible voters has been studied repeatedly and found to be false,” he said.

Mr. Kobach’s influential position on the panel intensified the controversy over its creation, particularly among immigration advocacy and civil rights groups, as well as Democrats who said they feared he would use the perch to try to prevent minority voters from casting ballots.

“Selecting Kris Kobach as vice chair reveals exactly the kind of discriminatory witch hunt the American people can expect from this commission,” said Representative Nancy Pelosi, Democrat of California and the House minority leader. “The president’s ‘election integrity’ commission is clearly intended to accelerate the vile voter suppression efforts in states across the nation.”

Mr. Kobach was the driving force behind a Kansas law requiring new voters to produce a passport, a birth certificate or naturalization papers as proof of citizenship. He worked last year to disqualify the state and local votes of thousands of people who did not meet those criteria. He has advocated the proof-of-citizenship requirement at the federal level as well, alleging rampant voter fraud without producing proof of a widespread problem.