Mr Barr had previously objected to a plan for lawyers to ask questions at Thursday's hearing. Committee chairman Jerrold Nadler accused the White House of a "complete stonewalling of Congress".
The standoff raises the prospect that Mr Barr, America's top legal official, could be held in contempt of Congress.
The Justice Department also said that it would not comply with a subpoena issued by Mr Nadler asking for an unredacted version of Mr Mueller's report as well as files from the investigation.
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