Earlier Tuesday, Trump intensified his fight with Congress by blocking Gordon Sondland, the U.S. European Union ambassador, from testifying behind closed doors about the president's dealings with Ukraine.
"He would be testifying before a totally compromised kangaroo court", Mr Trump said on Twitter.
"Secretary Pompeo's obstruction of the House's impeachment inquiry does not alleviate you of your independent legal obligation to produce to the Committees any responsive documents in your personal possession, custody, or control", the chairmen wrote.
House Speaker Nancy Pelosi has insisted the House is well within its rules to conduct oversight of the executive branch under the Constitution regardless of a vote.
Trump pressed Ukrainian President Volodymyr Zelenskiy in the July 25 call to investigate former Vice President Joe Biden and his son, Hunter - sparking a whistleblower complaint and now the impeachment inquiry.
The letter accuses Democrats of trying to change the 2016 election result, and attacks the investigation as "constitutionally invalid and a violation of due process".
White House lawyers, the report goes on to say, "initially believed it could be contained within the walls of the White House", though as the concerns escalated, a National Security Council lawyer directed the transcript be moved to a classified system, which CNN cites sources as saying was to prevent more people from seeing it, although one source raises the possibility that this was to "preserve" it.
Diplomatic text messages released by Democrats last week show that U.S. officials were involved in the effort to secure a public commitment from Ukraine to look into the business dealings of Hunter Biden.
"It is completely normal for the State Department to vet these messages before providing the copies to Congress", said the official.
Google is adding its Password Checkup feature directly into Chrome
The tool in question is essentially a check to determine whether passwords have been found in any breaches of a site or service. But Risher added we kind of suck at this categorisation - our words, not his - and end up reusing passwords when we shouldn't.
Why is there an impeachment inquiry?
Hunter, Mr Biden's son, once sat on the board of a Ukrainian energy company.
These claims have been widely discredited.
Progressive activists have been credited for keeping the heat on lawmakers to hold Trump accountable for his misconduct, and advocacy groups are continuing to mobilize to ensure House Democrats follow through with their inquiry.
The grounds for impeachment are sketchy, to say the least, and revolve around the word of a whistleblower whose allegations were based on secondhand information (hearsay) and who is allegedly against the president. A simple majority in the House's 435 members are needed to impeach the president, meaning that the members already supporting the inquiry are enough to kick the question over to the Republican-led Senate for a trial.
The Department of Defense and the White Office of Management and Budget must turn over the documents by October 15, they said.
The poll also showed 49 percent of Americans believe the House should call for the president to be removed from office, which would require conviction by the Senate.
Only two U.S. presidents in history - Bill Clinton and Andrew Johnson - were impeached but neither was convicted and removed.