WASHINGTON — President Trump’s commission on voter fraud, which has ricocheted between controversies since its creation in May, is scheduled to hold its second public meeting on Tuesday in New Hampshire. Already, the commission’s de facto leader has warmed up for the session by suggesting that the election in November of Senator Maggie Hassan, a New Hampshire Democrat, was rigged.

The accusation led the state’s entire congressional delegation to demand that William M. Gardner, the New Hampshire secretary of state, resign from the commission. Mr. Gardner, a Democrat and the host of the meeting on Tuesday, refused to do so, and said the state’s two senators and two representatives were being hypocritical.

Uproar has become standard practice for the fraud panel, officially called the Presidential Advisory Commission on Election Integrity. Critics say the commission is a pretext for Republican efforts to make it harder to register and to vote, and that it will reach a predetermined conclusion, that tough new rules are needed to prevent fraud. Studies have repeatedly shown that illegal voting is very rare, and that voter impersonation — perhaps the main danger suggested by advocates of tighter election rules — is next to nonexistent.

Since its formation, the commission has been accused of skirting open-government laws; it has publicly released personal details like street and e-mail addresses of citizens who contacted it, almost always to complain; and generated a fierce backlash when it asked state election officials to turn over data on every voter in the United States. The advocacy group Common Cause states in a new report that the request led more than 5,000 Colorado voters to de-register so that their personal information would not be sent to Washington.