The Democrat-led House of Representatives is set to vote next week on whether to hold Attorney General William Barr and former White House counsel Don McGahn in contempt of Congress for failing to comply with congressional subpoenas, House Majority Leader Steny Hoyer announced Monday.

Republicans repeatedly have countered that federal law protecting secretive grand-jury information would prevent Barr from turning over Special Counsel Robert Mueller's report. In a rare public statement last week, Mueller specifically remarked, "I certainly do not question the attorney general's good faith" in deciding to make the report "largely public."

As for McGahn, the White House has instructed its former top lawyer not to testify, saying he is legally immune from being compelled to testify about privileged discussions in the course of his official duties. Democrats have responded that McGahn waived that privilege by agreeing to speak to Mueller.

Trump did not assert executive privilege to shield any aspect of the Mueller report itself, and has derided Democrats' efforts as politically motivated attempts to keep what he's called the "Russia collusion hoax" alive -- and to distract from, or derail, Barr's own ongoing probes into Justice Department and FBI misconduct.

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News of the planned contempt vote came days after Barr said he has not received answers from the intelligence community that were "at all satisfactory" in the early stages of his review into the origins of the Russia investigation. Last month, Barr appointed U.S. Attorney from Connecticut John Durham to lead the investigation, which is to focus on the use of FBI informants and the alleged improper issuance of Foreign Intelligence Surveillance Act (FISA) warrants to monitor a variety of individuals, including former Trump aide Carter Page.

But, Hoyer, D-Md., said in a statement that the Trump administration's "systematic refusal to provide Congress with answers and cooperate with Congressional subpoenas is the biggest cover-up in American history, and Congress has a responsibility to provide oversight on behalf of the American people."

The vote would be historic, but not unprecedented. In 2012, the GOP-controlled House voted to hold then-Attorney General Eric Holder in contempt for failing to comply with investigations into the Obama administration's failed gun-running sting operation known as "Fast and Furious." Holder became the first-ever sitting Cabinet member to be held in contempt of Congress in that manner.

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The resolution scheduled for a June 11 floor vote would allow the Judiciary Committee to pursue civil action to seek enforcement of its subpoenas in federal court, Hoyer said. The House Judiciary Committee voted last month to hold Barr in contempt after he refused to turn over an unredacted version of Mueller's report.

Such an approach would rule out so-called "inherent contempt," a process in which Congress technically can enforce contempt citations on its own -- whether by arrest or fine. In May, Barr reportedly joked about that possibility with House Speaker Nancy Pelosi, D-Calif, asking, "Did you bring your handcuffs?"

"We're really doing this?" Texas Republican Rep. Dan Crenshaw asked Monday on Twitter, responding to the news. "We’re all supposed to just ignore the fact that Barr is bound by federal law to protect grand jury information? Are we pretending there might be some bombshell hidden in there? This is dishonest politics meant to discredit Barr."

The move came as Democrats have faced increased pressure from some of their members to launch impeachment proceedings against Trump. Some Democrats at a leadership meeting late Monday indicated they welcomed the contempt vote, according to people familiar with the private session, though it's unlikely to reduce calls for impeachment hearings against Trump.

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More than 40 House Democrats have called on House Judiciary Committee Chairman Jerry Nadler, D-N.Y., to start impeachment proceedings, which would make it easier for them to compel document production and testimony. But Pelosi so far has rejected that option, publiclly preferring a more methodical approach to investigating the president.

As part of that effort, Nadler said Monday that his panel will hold a series of hearings on "the alleged crimes and other misconduct" in Mueller's report, starting with a hearing June 10, the day before the planned contempt votes, on whether Trump committed obstruction of justice. The hearing is to feature John Dean, who was White House counsel for President Richard Nixon, and former U.S. attorneys.

The hearings are expected to serve as a stand-in of sorts for Mueller himself, who made clear in public comments last week that he did not want to appear before Congress and would not elaborate on the contents of his report if he were forced to testify. Democrats have suggested they would compel Mueller's appearance if necessary, but it's unclear when — or if — that would happen. Negotiations over Mueller's testimony were ongoing.

In the meantime, Democrats have been searching for ways to keep the spotlight fixed on Mueller's investigation — a challenge compounded by the White House's refusal to comply with requests for documents and testimony related to the report, which has stymied their investigations.

Mueller wrote that found no proof that the Trump team conspired with Russia to influence the 2016 elections, despite multiple overtures from Russian-affiliated individuals to the campaign. Mueller also investigated whether Trump tried to obstruct his investigation, but the report reached no conclusion on whether the president acted illegally.

Nadler said in a statement that Mueller "has now left Congress to pick up where he left off."

The special counsel reiterated in his remarks that, bound by Justice Department policy, charging a sitting president with a crime was "not an option." But, he also stressed he could not exonerate Trump. Instead, he said, "The Constitution requires a process other than the criminal justice system."

In a statement after Mueller's remarks, a spokesperson said the special counsel did not mean to contradict Barr's previous statement on the matter. Barr had said Mueller repeatedly assured him he was not saying that, "but for" Justice Department policy, "he would have found that the president obstructed justice."

Republicans criticized the decision to hold hearings, with North Carolina Rep. Mark Meadows calling the move "another openly desperate move to resuscitate a dead collusion conspiracy."

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"Thank goodness the Democrats are calling 'Watergate Star' John Dean to testify," Meadows tweeted sarcastically.

Dean ultimately cooperated with prosecutors and helped bring down Nixon's presidency, though he served a prison term for obstruction of justice.

Fox News' Brooke Singman, Chad Pergram and The Associated Press contributed to this report.