The former White House chief of staff is suing Pelosi and the members of the House select committee.
On Tuesday, his lawyer told the committee that he would no longer cooperate with the investigation.
The basis for the lawsuit was not clear. The committee subpoenaed him for documents and testimony, and it also subpoenaed his cell phone carrier to turn over the data.
The two overly broad and burdensome subpoenas were issued in whole or part without legal authority in violation of the Constitution and the laws of the United States, according to the request.
The complaint said that the Select Committee acts without any valid legislative power and threatens to violate longstanding principles of executive privilege and immunity. It was alleged that the subpoena violated the First Amendment rights.
The deposition that was scheduled for Wednesday is "untenable" because the committee has no intention of respecting boundaries related to former President Donald Trump's broad assertions of executive privilege.
The committee said it would recommend criminal contempt charges against him if he didn't show up for his deposition.
The January 6 investigatory panel member said last week that the argument for withholding information was undermined by the fact that he wrote about the Capitol riot in his new memoir.
He's spoken publicly about the Capitol riot, even though he can't give the select committee details because they're protected by executive privilege.
The former federal prosecutor said that if you talk publicly about matters you claim are privilege, you waive that privilege. Meadows can't answer questions about the same subject matter from Congress.
The committee has advanced or is prepared to advance contempt proceedings against three Trump allies. The Justice Department indicted former White House chief strategist Steve Bannon on two criminal contempt charges after Congress referred him. Jeffrey Clark, a former Justice Department official, is facing criminal contempt charges.
