(CNN) The White House flatly rejected the House Judiciary Committee's request for documents in its sweeping investigation into possible obstruction of justice , the latest escalation of tension in the battle between President Donald Trump's administration and the Democratic House conducting oversight of the Executive Branch.

In a move House Judiciary Chairman Jerry Nadler compared to "claiming that the President is a king," White House Counsel Pat Cipollone accused the committee in a letter sent Wednesday of seeking to recreate the special counsel investigation to harass the President.

"It appears that the Committee's inquiry is designed, not to further a legitimate legislative purpose, but rather to conduct a pseudo law enforcement investigation on matters that were already the subject of the Special Counsel's long-running investigation and are outside the constitutional authority of the legislative branch," Cipollone wrote.

"Congressional investigations are intended to obtain information to aid in evaluating potential legislation, not to harass political opponents or to pursue an unauthorized 'do-over' of exhaustive law enforcement investigations conducted by the Department of Justice," he added.

The letter adds yet another layer to the escalating feud between the White House and House Democrats over their numerous investigations into the Trump administration and President Donald Trump's businesses and finances.

Nadler responded to the latest Trump administration rejection by accusing the White House of "claiming that the President is a king."

"No President, no person in the United States is above the law. This is preposterous," Nadler told CNN. "They are saying we should end the investigation. We are not ending the investigation. If we were to agree to that, then no president would ever be subject to any kind of investigation for misconduct of any type."

Trump has already declared that his administration will fight all of the House subpoenas — several of which are now being fought in court. The Judiciary Committee voted last week to hold Attorney General William Barr in contempt for not providing the full Mueller report and evidence and the Ways and Means Committee has issued a subpoena for Trump's personal and business tax returns.

Democrats mull contempt and fines

Nadler and other House Democratic leaders are now raising the prospect they will hold numerous administration officials in contempt at the same time as part of a package to highlight the Trump administration's stonewalling of Congress. Some Democrats are also talking about invoking Congress' so-called inherent contempt powers to fine or jail those who defy congressional subpoenas.

Nadler told reporters Tuesday he was seriously considering the idea of fining officials.

"Very large," Nadler said when asked how large of fines the House might consider. Asked if they would seek to impose such fines on the attorney general, Nadler said: "It would be for anybody who is held in inherent contempt."

Other Democratic leaders appear less keen on the idea of inherent contempt, which Congress hasn't used in nearly a century.

"I don't think we're going to jail people and put them in the basement," House Majority Leader Steny Hoyer told reporters Wednesday, later arguing that Congress is "somewhat limited" in its ability to carry out inherent contempt, even though it has the authority.

In a holding tent at a US Capitol event Wednesday morning, Barr greeted House Speaker Nancy Pelosi and asked jokingly if she brought her handcuffs, according to two sources familiar with the exchange, making light of the inherent contempt threats.

One source said that Pelosi, "not missing a beat, smiled and indicated to the Attorney General that the House Sergeant at Arms was present at the ceremony should an arrest be necessary." Barr "chuckled and walked away," the source said.

Executive privilege fight

Cipollone's letter, which was first reported by The Washington Post , was sent in response to the document request the Judiciary Committee made in March to 81 individuals and entities , including the White House. The letters were the opening salvo in the panel's investigation into obstruction of justice and abuses of power, which covers many of the same topics as the Mueller investigation.

The requests also went to several former White House officials. The committee issued a subpoena for former White House counsel Don McGahn, and the White House instructed McGahn not to provide documents in response

McGahn has also been subpoenaed to testify on May 21, and Nadler is threatening to hold him in contempt if he does not appear.

In the letter, Cipollone accuses the House panel of violating executive privilege with the requests, although he did not say the White House had asserted privilege over the materials in question.

Though Trump has not formally asserted executive privilege, "it may come to that," a senior White House official told reporters Wednesday.

"If the Committee continues to pursue its inquiry, the requests in the Committee's March 4 letter suffer from numerous legal defects and reflect little, if any, respect for the legitimate interests of the Executive Branch or for the accommodation process that governs congressional requests for information from the Executive," Cipollone wrote.

Goading into impeachment?

The senior White House official said the administration remained open to working with Nadler on oversight requests as long as they serve a legitimate legislative purpose, but argued Nadler was "brushing aside the conclusions of the Justice Department in favor of political theater."

When asked for a response to Nadler saying Trump was asking more like a king, the official said it sounded like it was the committee who was acting "imperiously."

The official denied that the rejection of Nadler's request was an attempt to goad Congress into beginning impeachment proceedings — something Democrats have suggested the President is trying to do with his blanket rejection of congressional oversight.

Nadler on Wednesday said he didn't know the White House's motives, but he would not allow the White House to try to claim that the President cannot be held accountable.

"I don't know whether they're trying to taunt us toward an impeachment or anything else," Nadler said. "All I know is they have made a preposterous claim."