Former Special Counsel Robert Mueller testifies before the House Permanent Select Committee on Intelligence on Capitol Hill on Wednesday July 24, 2019 in Washington, DC.

A federal judge on Friday rejected claims that the impeachment probe of President Donald Trump is illegitimate as she ordered the Justice Department to give a House committee secret grand jury material collected in special counsel Robert Mueller's investigation.

That material could help the House Judiciary Committee substantiate "potentially impeachable conduct" by Trump, said Chief Judge Beryl Howell of U.S. District Court in Washington, D.C., in her ruling.

Howell brushed aside arguments made by Trump's supporters that the impeachment inquiry is illegitimate because the House has not held a formal vote authorizing such a probe.

"Even in cases of presidential impeachment, a House resolution has never, in fact, been required to begin an impeachment inquiry," the judge wrote.

She wrote that the White House's refusal to cooperate with the impeachment inquiry made it even more important to give the House panel the grand jury materials that it was seeking.

"Congress's need to access grand jury material relevant to potential impeachable conduct by a President is heightened when the Executive Branch willfully obstructs channels for accessing other relevant evidence," Howell said.

Earlier in October, White House counsel Pat Cipollone sent House leaders a letter that called the impeachment probe "baseless, unconstitutional efforts to overturn the democratic process."

Howell gave the Justice Department until next Wednesday to send to the Judiciary Committee the material sought, which is information collected by the grand jury that is referenced in or underlying the Mueller Report.

The Justice Department told CNBC that it is reviewing the ruling. The department is almost certain to appeal Howell's decision.

Grand jury material is, by law, normally kept secret.

But Howell wrote that "the need for continued secrecy is minimal and thus easily outweighed by [the Judiciary Committee's] compelling need for the material."

"Tipping the scale even further toward disclosure is the public's interest in a diligent and thorough investigation into, and in a final determination about, potentially impeachable conduct by the President described in the Mueller Report."

The Judiciary Committee, Howell said, "has shown that it needs the grand jury material referenced and cited in the Mueller Report to avoid a possible injustice in the impeachment inquiry" and "that this need for disclosure is greater than the need for continued secrecy."

House Judiciary Committee Chairman Jerry Nadler, D-N.Y., in a statement said, "I am gratified that the federal district court has ordered that the Special Counsel's grand jury information must be turned over to the House's impeachment inquiry."

"The court's thoughtful ruling recognizes that our impeachment inquiry fully comports with the Constitution and thoroughly rejects the spurious White House claims to the contrary," Nadler said. "This grand jury information that the Administration has tried to block the House from seeing will be critical to our work."

The House's ongoing impeachment inquiry is focused on Trump's recent pressuring of Ukraine to launch an investigation of former Vice President Joe Biden and his son Hunter Biden. Joe Biden is a leading contender for the Democratic nomination for president in 2020.

The president and his emissaries also have urged Ukraine to investigate a right-wing conspiracy theory that says Ukraine was either involved in or helped cover up a scheme to frame Russia for the hacking of Democratic National Committee computers in the runup to the 2016 U.S. presidential election.

At the time Trump was urging Ukraine's new president to open those investigations, the White House was withholding nearly $400 million worth of military aid to Ukraine.

Mueller's own 22-month-long investigation, which ended last March, probed Russian interference in the 2016 election, possible coordination with Russian agents by members of the Trump campaign, and possible obstruction of justice by Trump himself.

The special counsel concluded that Russia had actively interfered in the election with social media tactics and by releasing emails stolen from the DNC and from officials in Democratic nominee Hillary Clinton's campaign.

But Mueller also found that there was not sufficient evidence to charge people affiliated with the Trump campaign with conspiring with Russian agents to affect the election.

"We did not make a determination as to whether" Trump "did commit a crime," Mueller has said.