Secretary of State Mike Pompeo Michael (Mike) Richard PompeoWatchdog confirms State Dept. canceled award for journalist who criticized Trump Trump's push for win with Sudan amps up pressure on Congress Putin nominated for Nobel Peace Prize MORE on Tuesday warned that officials at his agency would not show up for scheduled depositions with House investigators, ramping up a heated battle with Democrats in their impeachment inquiry.

Democrats responded by arguing that Pompeo’s actions may constitute witness intimidation and obstruction of Congress’s investigation, which could be used as an argument for filing articles of impeachment.

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The chairmen of three House committees have requested depositions with five current and former State Department officials starting this week as part of their investigation into President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE’s efforts to pressure the Ukrainian government to investigate former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE and his son’s business dealings.

But Pompeo said in a letter to House Foreign Affairs Committee Chairman Eliot Engel Eliot Lance EngelHouse panel halts contempt proceedings against Pompeo after documents turned over Engel subpoenas US global media chief Michael Pack The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-N.Y.) on Tuesday that the scheduled dates offered insufficient time for all of the officials to prepare.

The chairmen — Engel, Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffSchiff to subpoena top DHS official, alleges whistleblower deposition is being stonewalled Schiff claims DHS is blocking whistleblower's access to records before testimony GOP lawmakers distance themselves from Trump comments on transfer of power MORE (D-Calif.) and Oversight and Reform Committee Chairman Elijah Cummings Elijah Eugene CummingsBlack GOP candidate accuses Behar of wearing black face in heated interview Overnight Health Care: US won't join global coronavirus vaccine initiative | Federal panel lays out initial priorities for COVID-19 vaccine distribution | NIH panel: 'Insufficient data' to show treatment touted by Trump works House Oversight Democrats to subpoena AbbVie in drug pricing probe MORE (D-Md.) — warned that refusing to comply with their demands could be used against Pompeo as evidence of obstruction.

“Any effort to intimidate witnesses or prevent them from talking with Congress — including State Department employees — is illegal and will constitute evidence of obstruction of the impeachment inquiry. In response, Congress may infer from this obstruction that any withheld documents and testimony would reveal information that corroborates the whistleblower complaint,” Engel, Schiff and Cummings said in a joint statement.

The chairmen also sent a letter to Deputy Secretary of State John Sullivan expressing their concern, saying Pompeo had "an obvious conflict of interest."

Pompeo said in his letter that the State Department “will be in further contact as we obtain further clarity on these matters” but said that the requested dates for depositions with State Department officials “are not feasible.”

“I’m concerned with aspects of your request ... that can be understood only as an attempt to intimidate, bully and treat improperly the distinguished professionals of the Department of State, including several career Foreign Service Officers,” Pompeo wrote.

Two former officials are still expected to appear before the committees in the coming days.

The depositions, which the three chairmen said would be conducted jointly by their committees, have been scheduled for this week and next.

The lawmakers are seeking depositions with five officials: Marie Yovanovitch, the former U.S. ambassador to Ukraine; Kurt Volker, Trump’s special envoy for Ukraine before resigning late last week; State Department Deputy Assistant Secretary George Kent; State Department counselor T. Ulrich Brechbuhl; and Gordon Sondland, the U.S. ambassador to the European Union.

All but Kent were mentioned in the whistleblower complaint.

Yovanovitch’s deposition, which had been scheduled for Wednesday, is now slated for Oct. 11, according to a House Intelligence Committee aide.

Volker, meanwhile, is expected to appear for his scheduled deposition on Thursday, the aide added.

It’s not yet clear if or when the other three will appear for depositions.

Democrats are hoping that the officials, starting with Volker, can help corroborate allegations made by the whistleblower about Trump trying to pressure Ukraine’s leader to help discredit a potential rival in the 2020 presidential election.

The intelligence community whistleblower alleged in the August complaint that Volker visited Kiev with Sondland a day after Trump’s July 25 phone call with Ukrainian President Volodymyr Zelensky and met with Ukrainian officials to discuss how to “navigate” Trump’s “demands.”

Yovanovitch, meanwhile, served as the ambassador to Ukraine until she was recalled from her post in May. Trump said in his call with Zelensky that Yovanovitch was “bad news,” according to the declassified rough transcript of the call released by the White House last week.

“The former ambassador from the United States, the woman, was bad news and the people she was dealing with in the Ukraine were bad news, so I just want to let you know that,” Trump said during the call.

Pompeo is also coming under scrutiny following reports that he was on Trump’s call with Zelensky.

“Secretary Pompeo was reportedly on the call when the President pressed Ukraine to smear his political opponent. If true, Secretary Pompeo is now a fact witness in the House impeachment inquiry. He should immediately cease intimidating Department witnesses in order to protect himself and the president,” the House committee chairmen said Tuesday.

The Foreign Affairs Committee, in consultation with the two other panels, had subpoenaed Pompeo for documents related to Trump pressuring the Ukrainian government to investigate Biden and his son Hunter Biden.

Pompeo said Tuesday that the State Department “intends to respond” by Friday.

The clash with Pompeo came a day after the Intelligence Committee, in coordination with Oversight and Reform and Foreign Affairs, subpoenaed Trump’s personal attorney, Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE, for documents related to his involvement in urging Ukrainian officials to investigate the Bidens.

Giuliani acknowledged during an interview with CNN’s Chris Cuomo Chris CuomoCNN's Don Lemon: 'Blow up the entire system' remark taken out of context CNN's Lemon: 'We're going to have to blow up the entire system' if Democrats win back White House, Senate Giuliani criticizes NYC leadership: 'They're killing this city' MORE on Sept. 19 that he asked the Ukrainian government to look into the Bidens, moments after initially denying it.

Whether Giuliani will comply with the subpoena is still unclear. He tweeted on Monday that the subpoena “raises significant issues concerning legitimacy and constitutional and legal issues,” but noted “it will be given appropriate consideration.”

As with Pompeo, the committee chairmen warned in a letter to Giuliani that defying the subpoena could be used as evidence of obstruction.

“Your failure or refusal to comply with the subpoena, including at the direction or behest of the president or the White House, shall constitute evidence of obstruction of the House’s impeachment inquiry and may be used as an adverse inference against you and the president,” the chairmen wrote.