Washington (CNN) House Democrats issued a stark warning to Secretary of State Mike Pompeo Tuesday after the top US diplomat accused lawmakers of "intimidating and bullying" State Department officials by calling them for depositions related to the Ukraine inquiry.

In a letter sent Tuesday afternoon, the chairmen of the House Intelligence, Foreign Affairs and Oversight committees told Pompeo that any effort to prevent those officials from speaking to Congress "is illegal and will constitute evidence of obstruction of the impeachment inquiry."

The response came just hours after Pompeo wrote to chairman of the House Foreign Affairs Committee, Rep. Eliot Engel of New York, notifying him that the proposed dates for depositions "do not provide adequate time for the Department and its employees to prepare" and that the request was "not feasible."

"I'm concerned with aspects of the Committee's request that can be understood only as an attempt to intimidate, bully, & treat improperly the distinguished professionals of the Department of State, including several career FSOs," he tweeted.

In a second tweet he added, "Let me be clear: I will not tolerate such tactics, and I will use all means at my disposal to prevent and expose any attempts to intimidate the dedicated professionals whom I am proud to lead and serve alongside at the Department of State."

I'm concerned with aspects of the Committee's request that can be understood only as an attempt to intimidate, bully, & treat improperly the distinguished professionals of the Department of State, including several career FSOs. pic.twitter.com/QRtMaXlhQM

The chairmen of the House Foreign Affairs, Intelligence and Oversight committees responded to Pompeo's letter later on Tuesday, saying that "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," said the statement from Reps. Adam Schiff of California, Engel and Elijah Cummings of Maryland.

The lawmakers also accused Pompeo of "intimidating Department witnesses in order to protect himself and the President," noting that he was on the President's July 25 phone call between Trump and the Ukrainian President and "is now a fact witness in the House impeachment inquiry."

And on Tuesday night, Schiff, Engel and Cummings sent a letter to Deputy Secretary of State John Sullivan claiming Pompeo "now appears to have an obvious conflict of interest" in the Ukraine inquiry due to his reported involvement in the phone call between Trump and the Ukrainian President.

"He should not be making any decision regarding witness testimony or document production in order to protect himself or the President," they wrote.

The letter comes after the State Department's inspector general requested an urgent briefing for Wednesday with senior congressional staff members, according to sources briefed on the matter. It's unclear exactly what the inspector general plans to provide Congress during the private Wednesday briefing.

Four of the five officials who the committee had scheduled to be deposed over the next two weeks -- Ambassador Marie "Masha" Yovanovitch, Ambassador Kurt Volker, Counselor T. Ulrich Brechbuhl and Ambassador Gordon Sondland -- were mentioned in the whistleblower complaint.

The fifth -- Deputy Assistant Secretary George Kent -- has overseen policy on Ukraine at the State Department since September 2018 and was previously the deputy chief of mission at the US Embassy in Ukraine.

Volker plans to appear

Volker, who resigned from his role at the State Department last week, is still planning to appear at his deposition Thursday in front of the three congressional committees, according to two sources familiar with his latest thinking. In a letter to trustees of the McCain Institute on Saturday where he serves as executive director, Volker wrote that Congress had requested his testimony and he would "be complying with that request."

However, it remains unclear whether the four current State Department officials will be deposed in the coming days by the committees, according to congressional sources.

On Friday, the three House committee chairmen subpoenaed Pompeo over his failure to produce documents related to "related to reported efforts by President Trump and his associates to improperly pressure the Ukrainian government to assist the President's bid for reelection."

"Pursuant to the House of Representatives' impeachment inquiry, we are hereby transmitting a subpoena that compels you to produce the documents set forth in the accompanying schedule by October 4, 2019," the chairmen of the House Foreign Affairs, Intelligence and Oversight committees wrote in a letter to Pompeo.

In their letters to Pompeo, the chairmen said that they found his refusal to comply with their earlier requests "all the more troubling" since "it has become clear that multiple State Department officials have direct knowledge of the subject matters of the House's impeachment inquiry."

In August, a State Department spokesperson confirmed that Volker, at the request of Ukrainian Presidential Adviser Andriy Yermak, had "put Yermak in direct contact" with Rudy Giuliani, Trump's personal lawyer.

"Mr. Giuliani is a private citizen and acts in a personal capacity as a lawyer for President Trump. He does not speak on behalf of the U.S. Government," the spokesperson said in a statement at the time.

Yovanovitch, who was unexpectedly recalled from her post in May 2019, was also mentioned in the White House rough transcript of President Donald Trump's July 25 call with Ukrainian President Volodymyr Zelensky.

"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 told Zelensky.

Yovanovitch, who was previously scheduled to appear on Capitol Hill this Wednesday, will now do so on October 11 with the agreement of both the Committees and counsel, a congressional aide told CNN Tuesday.

During that July 25 call, Trump asked Zelensky to speak with Giuliani and suggests that the Ukrainian President "look into" former Vice President Joe Biden and his son, Hunter.

"There's a lot of talk about Biden's son, that Biden stopped the prosecution and a lot of people want to find out about that so whatever you can do with the Attorney General would be great. Biden went around bragging that he stopped the prosecution so if you can look into it... It sounds horrible to me," Trump said, according to the White House transcript of the call.

There is no evidence of wrongdoing by Joe or Hunter Biden.

According to their complaint, the whistleblower "was told that a State Department official, Mr. T. Ulrich Brechbuhl, also listened in on the call." A State Department official has denied that Brechbuhl was on the call or briefed on it.

CNN reported Monday that Pompeo was also on that call despite previously denying knowledge of the whistleblower complaint.

The whistleblower said that a day after that call, Volker and Sondland "visited Kyiv and met with President Zelensky and a variety of Ukrainian political figures."

"Based on multiple readouts of these meetings recounted to me by various U.S. officials, Ambassadors Volker and Sondland reportedly provided advice to the Ukrainian leadership about how to 'navigate' the demands that the President had made of Mr. Zelenskyy," they wrote.

The whistleblower also said that the "multiple U.S. officials" told them that two ambassadors were among those "had spoken with Mr. Giuliani in an attempt to 'contain the damage' to U.S. national security."

Giuliani has denied the charges raised in the whistleblower complaint.