That prompted Republican lawmakers to move ahead on Thursday with a contempt of Congress resolution against Mr Garland.
James Comer, the oversight panel’s top Republican, said Mr Biden and his advisers “clearly fear” the release of the recordings “because it will again reaffirm to the American people that President Biden’s mental state is in decline”.
“The transcript of the interview was released months ago,” Harriet Hageman, who sits on the judiciary panel, wrote in a post on X.
“What is so damning in the audio that this administration is afraid to release them?”
By afternoon, her committee voted 18-15, entirely along partisan lines, to advance the resolution recommending that Mr Garland be held in contempt.
Mr Comer’s committee, however, postponed its own gathering until Thursday night.
Several of its Republican members have travelled to New York to show their support for Mr Trump in his ongoing criminal trial.
The contempt resolution – which would refer the country’s chief prosecutor for possible criminal charges – may ultimately go to a vote before the full House.
Republicans currently control the chamber by a single seat and it is unclear if they have the votes to hold Mr Garland in contempt.
If the attorney general is held in contempt, he will join his predecessors Bill Barr, who served in the Trump administration, and Eric Holder, of Barack Obama’s administration, in facing that fate.
Neither of those men faced criminal charges.