“There is a great deal the American public wants to know about the corruption of the Democrats,” Mr. Parscale said.

White House officials and a number of other defendants did not immediately comment on the lawsuit. Roger J. Stone Jr., a former campaign adviser to Mr. Trump who is named as a defendant in the suit, dismissed it in an email as “a left-wing conspiracy theory dressed up as a lawsuit.”

In a statement forwarded by Mr. Stone, Rob Buschel, Mr. Stone’s lawyer, said he had not yet been served with the D.N.C. suit and described it as a “regurgitation” of a complaint filed last year by Democrats alleging their privacy was invaded during the campaign. That litigation is still in progress.

The Democrats’ legal maneuver comes amid a swirl of intensifying scrutiny of Mr. Trump, his associates and their interactions with Russia. The president, who has long denied allegations of collusion, has repeatedly attacked the special counsel investigation this week and has vented angrily about renewed claims by James B. Comey, the former F.B.I. director, that Mr. Trump sought to influence the bureau’s review of the election.

Mr. Trump added Rudolph W. Giuliani, the former New York City mayor, and two other lawyers to his legal team this week. And on Thursday night, Mr. Trump thundered on social media that there was “NO COLLUSION and NO OBSTRUCTION,” and again branded the whole Russia investigation as a “witch hunt.”

The D.N.C. complaint is broad in its claims and stark in its language, naming a long list of defendants that includes Mr. Trump; his son, Donald Jr., and son-in-law, Jared Kushner; the Russian government and its intelligence service; and a group of former campaign aides including Mr. Stone, Paul Manafort, Rick Gates and George Papadopoulos.

There is substantial overlap between the targets of the D.N.C. lawsuit and the group of people known to be under investigation by Mr. Mueller. Mr. Manafort has been indicted by the special counsel, while Mr. Gates and Mr. Papadopoulos have both pleaded guilty to different charges.