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(CNN) —  

The House Judiciary Committee is planning to hold hearings on impeaching President Donald Trump that expand past the Ukraine investigation and wants former White House counsel Don McGahn to be forced to testify, according to a new court filing.

The judiciary panel on Tuesday asked a federal judge to make a ruling quickly on whether McGahn must testify in the House impeachment inquiry, citing a “finite window of time” when he’s needed.

A quick ruling siding with the House could yield major new impeachment witnesses about the Mueller investigation, Ukraine and obstruction of justice from people who worked in the White House and have thus far refused to testify.

“The Judiciary Committee anticipates holding hearings after HPSCI’s public hearings have concluded and would aim to obtain Mr. McGahn’s testimony at that time,” the committee wrote, referring to the impeachment inquiry hearings led by the House Intelligence Committee. “Thus, there is an urgent need for final resolution of the matter now pending before this Court.”

The House’s letter to federal Judge Ketanji Brown Jackson in Washington points out that it is considering impeaching Trump for obstruction of justice, for which McGahn would be a key witness since he spoke to special counsel Robert Mueller for the obstruction investigation, and for lying to Mueller, after testimony at Roger Stone’s criminal trial raised questions about Trump’s written answers to investigators about Russian interference in the 2016 election.

Jackson said she will rule by the end of the day Monday.

The House wrote it has an “urgent need for Defendant Donald McGahn’s testimony for use in the House’s impeachment inquiry and the mounting broader ramifications of a ruling in this case for that quickly progressing inquiry.” Jackson already has heard arguments on McGahn’s case.

The White House stopped McGahn from testifying last spring, citing “absolute immunity” over its high-level former officials.

The question of whether Trump lied to Mueller, the House notes, has become more pressing since his former deputy campaign chairman testified in court last week that Trump expected information after speaking with Stone, who was pursuing details from WikiLeaks in 2016 that could help Trump’s campaign. The House general counsel said before a federal appellate court Monday that the House is now investigating Trump for possibly lying.

A lying or obstruction investigation by the Judiciary Committee would be separate from the current House Intelligence Committee-led investigation regarding Ukraine.

However the judge resolves McGahn’s case could have significant implications for the Ukraine impeachment inquiry – including whether top former White House officials such as former national security adviser John Bolton decide to testify. The White House has used claims of immunity to stop some executive branch witnesses from testifying under subpoena about Mueller and in the Ukraine impeachment inquiry.

In the Ukraine inquiry, Bolton’s former national security deputy, Charles Kupperman, went to court in late October asking for help deciding whether he should testify. That case may not be resolved until mid-December or January, and the House has asked Kupperman to follow the court’s decision in the McGahn case. But Kupperman’s lawyer, who also represents Bolton, said the cases aren’t the same – because McGahn would be speaking about events that aren’t necessarily national security. Neither Bolton nor Kupperman is under subpoena at this time.

This story has been updated.