The Justice Department has told the House Judiciary Committee it has objections over the format of planned questioning, according a Democratic senior committee aide.
The department disapproves of plans to allow committee lawyers from both sides to question Mr Barr after the traditional round of questioning by committee members.
Justice officials also told the committee they are opposed to the panel’s plan to go into a closed session if members want to ask about redacted portions of the Mueller report, the anonymous aide said.
House committee chairman Jerry Nadler has threatened to use subpoena powers should the attorney general refuse to attend this week.
The New York Democrat told CNN that Mr Barr would not “dictate the format … the witness is not going to tell the committee how to conduct its hearing”.
Asked what would happen if the attorney general refused to testify on Thursday, Mr Nadler replied that they would "have to subpoena him, and we will have to use whatever means we can to enforce the subpoena.”
The Justice Department declined to comment on the dispute.
Mr Barr is also scheduled to testify before the Senate Judiciary Committee on Wednesday, but the Republican-led Senate committee is expected to have more traditional rounds of member questioning.
It is unusual for committee counsels to question a witness, but committees can generally set their own rules. During Supreme Court Justice Brett Kavanaugh’s confirmation hearing last year, Republicans on the Senate Judiciary Committee hired an outside prosecutor to question a witness who had accused him of sexual assault.
Mr Trump's aide Kellyanne Conway said the president could use executive privilege to block former White House lawyer Don McGahn from complying with a subpoena requiring him to testify before the House Judiciary Committee.
The Democratic-led committee served Mr McGahn with a subpoena almost a week ago, as it investigated whether the president obstructed justice.
House Democrats and the Trump administration remain at odds over full access to Mr Mueller’s report, having also subpoenaed the Justice Department for the unredacted version of the Mueller report and underlying material gathered from the investigation.
In response, the Justice Department has said they will make the full report, minus grand jury material, available to a limited group of members – an offer that Democrats have so far refused. Experts have predicted the dispute will eventually end up in court.
A spokeswoman for the top Republican on the committee, Rep. Doug Collins of Georgia, noted that Mr Barr’s testimony is voluntary.
“Democrats have yet to prove their demands are anything but abusive and illogical in light of the transparency and good faith the attorney general has shown our committee,” said Jessica Andrews.
Democrats have criticised Mr Barr for drawing his own conclusion that Mr Trump did not obstruct justice, despite the Mueller report concluding he could not be exonerated on that point.
Additional reporting by Associated Press
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