Late Monday afternoon, House Judiciary Committee Chairman Rep. Jerry Nadler said his committee would meet as planned Tuesday morning and McGahn was expected to appear.
"The Mueller Report documents a shocking pattern of obstruction of justice," Nadler said in a statement. "The President acted again and again -- perhaps criminally -- to protect himself from federal law enforcement.
"Don McGahn personally witnessed the most egregious of these acts. President Trump knows this. He clearly does not want the American people to hear firsthand about his alleged misconduct, and so he has attempted to block Mr. McGahn from speaking in public tomorrow."
In a letter to Nadler, the attorney for McGahn said he "remains obligated to maintain the status quo and respect the president's instructions. In the event an accommodation is agreed between the Committee and the White House, Mr. McGahn will of course comply with that accommodation."
Earlier, in a letter to Nadler, White House counsel Pat Cipollone wrote "that McGahn is absolutely immune from compelled congressional testimony with respect to matters occurring during his service as a senior adviser to the President," citing previous Department of Justice Office of Legal Counsel opinions, along with OLC guidance specific to McGahn's testimony.
"The immunity of the President's immediate advisers from compelled congressional testimony on matters related to their official responsibilities has long been recognized and arises from the fundamental workings of the separation of powers. Those principles apply to the former White House Counsel," the Office of Legal Counsel opinion on McGahn reads. "Accordingly, Mr. McGahn is not legally required to appear and testify about matters related to his official duties as Counsel to the President."
Because of this "constitutional immunity," Cipollone wrote, "the President has directed Mr. McGahn not to appear at the Committee's scheduled hearing on Tuesday, May 21, 2019."
"The Department of Justice has provided a legal opinion stating that, based on long-standing, bipartisan, and Constitutional precedent, the former Counsel to the President cannot be forced to give such testimony, and Mr. McGahn has been directed to act accordingly. This action has been taken in order to ensure that future Presidents can effectively execute the responsibilities of the Office of the Presidency," press secretary Sarah Sanders said in a statement.
"The Democrats do not like the conclusion of the Mueller investigation -- no collusion, no conspiracy, and no obstruction -- and want a wasteful and unnecessary do-over," she said.
Nadler rejected those arguments.
"This move is just the latest act of obstruction from the White House that includes its blanket refusal to cooperate with this Committee," his statement continued. "It is also the latest example of this Administration's disdain for law. This identical approach was rejected by a federal court in the Miers case, which held that even senior advisers to the President cannot simply refuse to appear in response to a congressional subpoena.
"It is absurd for President Trump to claim privilege as to this witness's testimony when that testimony was already described publicly in the Mueller Report. Even more ridiculous is the extension of the privilege to cover events before and after Mr. McGahn's service in the White House," Nadler said.
Earlier this month, the White House instructed McGahn not to comply with a subpoena from House Democrats for documents related to Mueller's investigation.
Cipollone argued at the time that "McGahn does not have the legal right to disclose these documents to third parties" and asked that instead of directing requests for documents to McGahn's attorney, the committee direct the requests to the White House.
McGahn was a central figure in the Mueller report and cooperated extensively with the special counsel's probe. He met with Mueller's team multiple times for more than 30 hours and questioned more extensively than any other member of the White House staff who went in for an interview.
"Mr. McGahn is a critical witness to many of the alleged instances of obstruction of justice and other misconduct described in the Mueller report," Nadler wrote last month in a press release accompanying his subpoena request. "His testimony will help shed further light on the President's attacks on the rule of law, and his attempts to cover up those actions by lying to the American people and requesting others do the same."
Mueller had requested to speak with McGahn about the circumstances surrounding former FBI Director James Comey's firing and his reported involvement in the events surrounding Attorney General Jeff Sessions' recusing himself from the Russia investigation, the sources said.
ABC News previously reported that McGahn was among the White House staffers who were against any notion of Trump's firing of Mueller last June when the president wanted to do just that, a source said.
After news broke that Trump ordered McGahn to fire the special counsel, Trump pressured McGahn to deny that he had been directed to do so, even suggesting to aides that he would fire him unless he complied.
Mueller concluded that there is evidence to suggest Trump acted this way to impede his investigation, according to the special counsel's report.
Mueller concluded that "Substantial evidence indicates that in repeatedly urging McGahn to dispute that he was ordered to have the Special Counsel terminated, the President acted for the purpose of influencing McGahn's account in order to deflect or prevent further scrutiny of the President's conduct towards the investigation."
There is precedent for past administrations to declare immunity from congressional testimony based on an Office of Legal Counsel opinion. For example, in 2014, the Obama administration blocked senior adviser and director of the White House Office of Political Strategy, David Simas, from testifying before the House Oversight Committee.
ABC News' Benjamin Siegel contributed to this report.