Still smarting from a backlash by state election officials, the White House panel investigating claims of voter fraud and other irregularities was hit with a salvo of lawsuits on Monday that accused it of violating federal privacy laws and illegally operating in secret.

Three lawsuits, filed separately by civil rights groups, underscored the depth of opposition by the Trump administration’s critics to the panel, the Advisory Commission on Election Integrity, even before it formally meets. The commission’s official mandate is to look at flaws in federal voting systems and practices that could encourage fraud and undermine public confidence in elections.

But advocacy groups and many Democratic leaders have called it a Potemkin exercise intended to validate President Trump’s groundless claim that millions of illegal ballots cost him a popular-vote victory in November. The true goal, they say, is to lay the groundwork for Congress to place strict qualifications on registering and voting that would primarily suppress opposition to Republican candidates for office.

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The commission drew a bipartisan rebuke last week after its vice chairman and de facto leader, Kris Kobach, the Kansas secretary of state, asked officials in 50 states and the District of Columbia to voluntarily provide personal records so that they could be matched against one another and against other databases, apparently to search for evidence of illegal voting. No state has complied with the entire request, in part because laws mandate that personal records be kept private, and many states have refused to participate at all.

Mr. Kobach, who has said Mr. Trump’s claim that he was robbed of a popular-vote victory is plausible, is among the leading advocates of restrictions on voting and registration.

“This is a shoddy commission, and the stakes are high,” said Kristen Clarke, the president of the Lawyers’ Committee for Civil Rights Under Law, a voter advocacy group. “They seek data on more than 200 million registered voters across the country. At the least, they should be complying with federal legal requirements” governing the commission’s functions.

The Lawyers’ Committee suit and a similar one by the American Civil Liberties Union accused the commission of violating the Federal Advisory Committee Act, which sets standards for openness and accountability by such committees. The groups say that the commission has already held one telephone consultation that violated federal open-meeting requirements and that it refused to turn over working papers and other documents that by law should be available for public inspection.

They also argue that the commission’s proclaimed first meeting, on July 19, will be viewable only on the internet, violating the law’s requirement that it be held in a place open to “a reasonable number of interested members of the public.”

A third suit, by the advocacy group Public Citizen, argues that the commission is violating the federal Privacy Act by designating the Army to collect data on voters’ registrations and voting histories and other identifying data, including partial Social Security numbers and birthdates. The group said that law barred the federal government from collecting or using any “record describing how any individual exercises rights guaranteed by the First Amendment,” which covers voting and other forms of political expression.

A similar suit, filed a week ago by the Electronic Privacy Information Center, said the commission’s request violated the 2002 E-Government Act, which requires the government to publicly assess the consequences of its actions before seeking personal information stored electronically.