House Speaker Nancy Pelosi said Monday the House will vote this week on a resolution to formalize -- and establish the parameters -- of the Trump impeachment inquiry.

In a letter sent to Democratic House lawmakers, Pelosi, D-Calif., said the resolution "affirms the ongoing, existing investigation" and "establishes the procedure" for future investigative steps.

“We are taking this step to eliminate any doubt as to whether the Trump administration may withhold documents, prevent witness testimony, disregard duly authorized subpoenas, or continue obstructing the House of Representatives," Pelosi said.

Fox News has learned the vote will take place Thursday on the House floor.

It is not an actual article of impeachment, but rather a resolution that sets process ground rules.

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Republicans hit back Monday at Pelosi over the planned vote, with South Carolina Sen. Lindsey Graham -- the chairman of the Senate Judiciary Committee, which would play a role in a Senate impeachment trial -- saying, “A vote now is a bit like un-ringing a bell as House Democrats have selectively leaked information in order to damage President Trump for weeks."

House Minority Leader Kevin McCarthy, R-Calif., told Fox News: "What it authorizes is that we were right. You can’t go back now."

The White House argued Monday that the move proves Democrats have been conducting an "unauthorized" inquiry.

“We won’t be able to comment fully until we see the actual text, but Speaker Pelosi is finally admitting what the rest of America already knew – that Democrats were conducting an unauthorized impeachment proceeding, refusing to give the President due process, and their secret, shady, closed-door depositions are completely and irreversibly illegitimate,” White House press secretary Stephanie Grisham said in a statement.

Republicans for weeks have called for a formal House vote, challenging the legitimacy of the current framework for impeachment proceedings in the absence of one. Earlier this month, the White House wrote a defiant eight-page letter to Pelosi and top Democrats saying it would not cooperate with the impeachment inquiry.

"I take pride in the fact that our vigorous response to their underhanded tactics ended up making the House Democrat position untenable," Graham said Monday. "Today, they were forced to change course."

Pelosi made clear in her letter that the vote is being conducted because of the Republican complaints. She accused Trump and his GOP allies of holding the position that "because the House has not taken a vote, they may simply pretend the impeachment inquiry does not exist."

Even as she announced a formal vote, Pelosi insisted Monday that this argument "has no merit."

“This resolution establishes the procedure for hearings that are open to the American people, authorizes the disclosure of deposition transcripts, outlines procedures to transfer evidence to the Judiciary Committee as it considers potential articles of impeachment, and sets forth due process rights for the president and his counsel,” she said.

In a statement, California Rep. Adam Schiff, the chairman of the House Permanent Select Committee on Intelligence and a key Democrat involved in the inquiry, said: "This week, we will bring to the floor a resolution that establishes the format for open hearings that will be conducted by the House Intelligence Committee as part of the House’s ongoing impeachment inquiry, as well as procedures to transmit any evidence or report to the Judiciary Committee. The American people will hear firsthand about the president's misconduct.”

Just two weeks ago, Pelosi met with the Democratic caucus and said that there would be no formal vote at that point on the launch of formal impeachment proceedings, despite the GOP pressure. But Democrats said Pelosi is now embracing a vote for strategic reasons.

“She wants to nullify their process argument,” a senior Democratic source told Fox News. “That’s all they talk about. Republicans won’t touch the substance. So this is her way of forcing their hand.”

On Wednesday, the Democratic chairman of the Rules Committee, Massachusetts Rep. James McGovern, said the committee will mark up the impeachment procedure resolution Wednesday. Fox News is told that the resolution should be available for review Tuesday but is not yet complete.

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“As committees continue to gather evidence and prepare to present their findings, I will be introducing a resolution to ensure transparency and provide a clear path forward, which the Rules Committee will mark up this week. This is the right thing to do for the institution and the American people,” McGovern said.

Pelosi on Sept. 24 announced the formalization of the Trump impeachment inquiry, saying at the time that "the president must be held accountable" for his "betrayal of his oath of office, betrayal of our national security, and the betrayal of the integrity of our elections."

The inquiry was opened after a whistleblower complaint alleged that Trump, during a July phone call, pushed Ukrainian President Volodymyr Zelensky to investigate former Vice President Joe Biden and his son Hunter as military aid to the country was being withheld.

Fox News' Chad Pergram, Mike Emanuel and Brooke Singman contributed to this report.