Attorney General William Barr is threatening not to testify before the House Judiciary Committee this week because of concerns about the hearing's format, a senior Democratic aide on the committee has told NBC News.

The Department of Justice threatened that Barr would not attend the hearing because of new conditions placed on him over his testimony, the aide said. The House Judiciary Committee wants to be able to go into executive session with Barr, which would be closed to the press and public, to ask about portions of special counsel Robert Mueller's redacted report and also have the Democratic and Republicans committee counsels ask questions for 30 minutes after each lawmaker completes his or her allotted five minutes of questioning.

House Judiciary Committee Democrats discussed these additional requests last week and most recently spoke with the Justice Department about them on Friday afternoon, the aide said. It's unclear what will happen regarding Barr's testimony or whether he will attend the Thursday hearing, which is slated to take place a day after he appears before the Senate Judiciary Committee.

Justice Department spokeswoman Kerri Kupec told NBC News in a statement, "The attorney general agreed to appear before Congress. Therefore, members of Congress should be the ones doing the questioning. He remains happy to engage with members on their questions regarding the Mueller report."

Jessica Andrews, a spokesperson for the House Judiciary Republicans, told NBC News that Barr had voluntarily offered to testify before the committee, in addition to voluntarily making the redacted report public and offering House Democrats the chance to view a less-redacted report in person.

"Yet the only thing, apparently, that will satisfy Democrats, who refuse to read the less-redacted report, is to have staff pinch hit when a Cabinet official appears before us," Andrews said. "What actual precedent is there for our committee making such demands of a sitting attorney general as part of our oversight duties?"

"The attorney general isn’t a fact witness, and this committee’s investigations — as Democrat leadership reminds us daily — don’t constitute impeachment, so Democrats have yet to prove their demands anything but abusive and illogical in light of the transparency and good faith the attorney general has shown our committee," Andrews continued.

If Barr skips the hearing, it would mark the latest escalation in tensions between the Trump administration and House Democrats, who are requesting access to Mueller's full, unredacted report.

Last week, President Donald Trump said his administration was "fighting all the subpoenas" from House Democrats. The comment came after Nadler's committee subpoenaed former White House counsel Don McGahn to testify on his comments in the Mueller report. In the report, McGahn details at length Trump's efforts to have the then-White House counsel oust Mueller.

Trump called that subpoena "ridiculous," adding, "These aren’t, like, impartial people."

"The Democrats are trying to win 2020," the president continued.

On Sunday, House Judiciary Committee Chairman Jerrold Nadler, D-N.Y., said Barr would not "dictate the format of the Judiciary Committee," CNN reported.

"The witness is not going to tell the committee how to conduct its hearing, period," Nadler said, adding that if Barr does not appear on Thursday, his committee "will have to subpoena him, and we will have to use whatever means we can to enforce the subpoena."