Former Trump White House chief of staff Mark Meadows is suing the House select committee investigating January 6 and House Speaker Nancy Pelosi, asking a federal court to block enforcement of the subpoena the committee issued him as well as the subpoena it issued to Verizon for his phone records, according to the complaint filed Wednesday. The lawsuit comes after the committee signaled it would pursue a criminal contempt referral against Meadows because of his refusal to sit for a deposition in the investigation into the Capitol riot. Meadows alleges that the subpoenas are “overly broad and unduly burdensome,” while claiming that the committee “lacks lawful authority to seek and to obtain” the information requested. Republican Rep. Liz Cheney of Wyoming, who serves as vice chair of the panel, told CNN Wednesday evening, “We look forward to litigating that.” Cheney noted that Meadows is refusing to answer questions about documents that he turned over voluntarily. “The committee has received a number of extremely interesting, non-privileged documents from Mr. Meadows. These include text messages and emails from his private cell phone and private email account. He’s produced these documents, they are not privileged,” she said. “They include documents that are directly related to what President Trump should have been doing on January 6 during the attack, and now he is refusing to appear to answer questions about those non-privileged documents.” The lawsuit points to President Joe Biden’s refusal to assert executive privilege, which former President Donald Trump has sought, in the investigation – a dispute currently being litigated in a separate case Trump has brought seeking to block the release of his White House records to House investigators. “As a result, Mr. Meadows, a witness, has been put in the untenable position of choosing between conflicting privilege claims that are of constitutional origin and dimension and having to either risk enforcement of the subpoena issued to him, not merely by the House of Representatives, but through actions by the Executive and Judicial Branches, or, alternatively, unilaterally abandoning the former president’s claims of privileges and immunities,” Meadows’ lawsuit said. RELATED: New details shed light on ways Mark Meadows pushed federal agencies to pursue dubious election claims The lawsuit additionally alleges that the Verizon subpoena violates both the Constitution and the Stored Communications Act. Select Committee Chairman Bennie Thompson said he plans to move ahead next week with a criminal contempt referral. “I’m not a lawyer or judge and we’ll see what happens,” said the Mississippi Democrat, who added he had not reviewed the suit in great detail. “But we have every intention to move forward with the contempt citation.” Thompson rejected claims in the lawsuit that the committee was without merit and therefore had no right to access the personal information of its subpoena targets. “Well, you know, in this town, every lawyer has at least one opinion,” Thompson said. “We have authority because we were created by the House of Representatives.” When asked if he thought the lawsuit was a stall tactic by Meadows and his legal team, Thompson replied flatly: “Yes.” Rep. Adam Schiff, a California Democrat who is a member of the committee and one of the defendants named in the lawsuit, said the suit “certainly strikes me as another fruitless effort to impede the work of the committee.” The committee’s Meadows subpoena sought 27 categories of records, according to the complaint – most of them having to do with the effort by Trump and his allies to overturn the election results as well as communications specific to the events of January 6. The subpoena additionally demanded that Meadows sit for a deposition. While Meadows did produce some of the requested documents, he and the committee entered a standoff over the deposition, with Meadows claiming in the lawsuit that the committee refused to negotiate with him in good faith to accommodate his concerns around executive privilege and testimonial immunity. Meadows ultimately reached an agreement with the committee to appear voluntarily for a deposition Wednesday, his lawsuit said, but then he was “blindsided” last week by a notification from Verizon that it had been subpoenaed for metadata from the personal cell phone he used while White House chief of staff. Documents turned over earlier Prior to Meadows’ recent decision to halt cooperation with the committee, he had turned over approximately 6,000 pages worth of documents. That includes information from his personal email account and personal cell phone that are relevant to the committee’s investigation. In one November 6, 2020, text exchange with a member of Congress, Meadows reportedly said “I love it” in a discussion about the possibility of appointing alternate electors in certain states, and the member acknowledged the plan would be “highly controversial.” The committee also has in its possession a text exchange between Meadows and an organizer of the January 6 rally that preceded the riot from early January 2021, and text messages about the need for Trump to issue some kind of a public statement to stop the January 6 attack on the Capitol. Meadows has not indicated he will claim 5th Amendment protections, but multiple witnesses subpoenaed by the committee, including Trump ally Roger Stone and former Justice Department official Jeffrey Clark, have said they intend to do so. This story has been updated with additional developments Wednesday.