Former FBI Director Robert Mueller at the US Capitol in Washington, DC on June 21, 2017.

His comment comes as House Democrats escalate their fight with the Justice Department over the unredacted version of the special counsel's report on Russian election interference and potential obstruction of justice by Trump.

"It's Bob's call whether he wants to testify," Barr said, the Journal reported early Thursday.

Robert Mueller will decide whether he will testify to Congress, Attorney General William Barr told The Wall Street Journal. President Donald Trump had earlier said that it would be up to Barr to decide whether Mueller would testify.

Previously, the president had said Mueller shouldn't testify. Trump has repeatedly claimed that the Mueller report exonerated him. However, on the question of obstruction, Mueller said he did not exonerate the president. Barr, along with now-departed Deputy Attorney General Rod Rosenstein, decided not to charge Trump with any obstruction crimes.

The attorney general has been at odds with House Democrats, particularly Judiciary Committee Chairman Jerry Nadler of New York, who is continuing to seek Mueller's testimony.

In an interview with CNBC's John Harwood, Nadler said: "Bill Barr is just a liar. And, he's just representing the president."

Nadler's committee voted to hold Barr in contempt for refusing to comply with a subpoena for the unredacted Mueller report. Trump had asserted executive privilege over the full report. A redacted version of the document was released to the public in April. Mueller completed his probe in March.

The White House, likewise, is waging its own battle with House Democrats. White House lawyer Pat Cipollone warned Nadler and his colleagues not to "pursue an unauthorized 'do-over'" of the special counsel's probe, calling for the Judiciary Committee to "discontinue the inquiry."

Nadler rejected the White House's demand. "Our investigation into this as well as other troubling conduct by this administration will continue," he said.

A spokesman for the special counsel declined to comment.

WATCH: Rep. Jerry Nadler says Bill Barr 'just a liar'