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 on Wednesday said he might be willing to cooperate with House Democrats' impeachment inquiry, but only if they hold a formal vote to outline rules for the investigation and if those rules "are fair."

Trump was asked twice during an event in the Roosevelt Room of the White House if he would cooperate with Democrats leading the impeachment inquiry.

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“We would if they give us our rights. It depends," Trump said initially, indicating that he would not be inclined to cooperate with the probe if Democrats "say you can’t have lawyers, you can’t ask questions, you can’t have anybody present, all of these crazy things."

Asked again to clarify his position, Trump reiterated that he would collaborate with Democrats "if the rules are fair."

White House counsel Pat Cipollone on Tuesday night sent a letter to Speaker Nancy Pelosi Nancy PelosiDemocratic senator to party: 'A little message discipline wouldn't kill us' Overnight Health Care: New wave of COVID-19 cases builds in US | Florida to lift all coronavirus restrictions on restaurants, bars | Trump stirs questions with 0 drug coupon plan Overnight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds MORE (D-Calif.) and three committee leaders stating that the administration would not cooperate with any of their requests related to the impeachment inquiry.

The White House decried the impeachment inquiry as an "invalid" effort to "overturn the results of the 2016 election" and asserted that the lack of a formal vote to start the investigation broke with past precedent and violated the executive branch's rights.

Pelosi announced late last month that the House would formally launch the inquiry into Trump, alleging he abused his office by urging Ukraine's president to “look into” Democratic presidential candidate 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.

Pelosi has noted that there is no legal obligation for the House to formally vote to authorize the impeachment inquiry. Some Democrats and Republicans have said they believe there should be a vote, however.

Democratic committee leaders have in recent days issued subpoenas demanding records from the White House, Vice President Pence, the Office of Management and Budget, the Pentagon and Trump’s personal lawyer 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 as part of the investigation.

Top Democrats have warned that the White House's refusal to comply with their requests could be cited as obstruction in a potential article of impeachment.