GOFFSTOWN, N.H. — The vice chairman of President Trump’s election integrity commission on Tuesday again attempted to cast doubt on the outcome of the November election in New Hampshire, arguing that until the state’s voter database is analyzed further, “we will never know the answer to the legitimacy of that particular election.’’

The charge, made by Kansas Secretary of State Kris Kobach, drew protests from New Hampshire Secretary of State Bill Gardner, a member of the commission who insisted the state’s election results were “real and valid.’’

The exchange took place at a meeting of the Presidential Advisory Commission on Election Integrity, which gathered in New Hampshire Tuesday to take testimony on voter turnout and investigate whether widespread voter fraud exists.

The controversial panel traces its origins to last winter, when President Trump claimed there was widespread voter fraud in the November election, at one point saying that between 3 million and 5 million illegal votes nationwide caused him to lose the popular vote to Democrat Hillary Clinton.

He also singled out New Hampshire — arguing that he would have won the state in the general election if not for “busloads’’ of out-of-state residents voting. He made the claim without providing proof that such buses or voter fraud existed.

Critics have called the commission a “sham,’’ pointing to decades of research that says no widespread fraud exists. They suggest the commission is a front to pass new election laws to restrict voting.

Last week, Kobach renewed the New Hampshire election controversy, saying he had proof that the state had voted for Hillary Clinton for president and elected Democrat Maggie Hassan to the US Senate only because more than 5,000 people had voted unlawfully.

He pointed to data showing that they had provided out-of-state driver’s licenses at the polls and have yet to update those licenses, even though new residents are required to do so within 60 days of moving to the state. (Kobach did not note that many of those residents could be out-of-state college students, who are still eligible to vote. An analysis by New Hampshire Public Radio found that highest rates of voters using out-of-state identification voted in college towns, such as Durham and Hanover.)

At Tuesday’s meeting, Maine Secretary of State Matt Dunlap defended New Hampshire.

“Making this equation that somehow people not updating their driver’s licenses is indicative of voter fraud is as absurd as saying that if you have cash in your wallet, you robbed a bank,’’ he said.

Later, commission member Hans von Spakovsky, a researcher at the conservative Heritage Foundation, gave unsolicited advice to Gardner about what “should obviously be done’’ now in New Hampshire. He suggested Gardner contact other states and ask about individuals who used out-of-state identification.

“Until you do that investigation you don’t know what is going on,’’ von Spakovsky said.

Gardner responded with a stoic stare.

The commission met at the New Hampshire Institute of Politics at Saint Anselm College, a campus where both Clinton and Trump campaigned during both the primary and general elections. Outside, more than 100 protesters held signs and chanted, “Hey hey, ho ho, this sham commission has got to go.’’ Potential presidential candidate Jason Kander, a Democrat and the former Missouri secretary of state, held a press conference outside to criticize the commission.

Also Tuesday, a Nashua judge struck down parts of a new voting law backed by the Republican Legislature and governor aimed at cracking down on out-of-state voters.

Locally, political pressure has been mounting for Gardner to end his participation on Trump’s election commission. Gardner, a Democrat, is the nation’s longest-serving secretary of state and has been revered as the keeper of the state’s first presidential primary. All members of the state’s federal delegation called on Gardner to quit the panel.

“Some are questioning why I am here,’’ Gardner said at the opening of the meeting Tuesday. “New Hampshire people aren’t accustomed to walking away or stepping down from their civic duty, and I will not either.’’

While Gardner said his participation on the presidential commission is a public service, US Senator Jeanne Shaheen, a New Hampshire Democrat, said, she was “concerned that reckless accusations of widespread voter fraud and illegitimate elections in New Hampshire could jeopardize our state’s first-in-the-nation presidential primary.’’

But New Hampshire state Representative David Bates, a Republican, argued that the panel served a useful purpose. “As much as the left wants to say this is just about voter suppression, commissions like these are important because we have to figure out the facts first and not just put our head in the sand,’’ he said.

James Pindell can be reached at james.pindell@globe.com.