US District Judge Carl Nichols quickly denied that motion from Mr Bannon's lawyers, but indicated that he might grant a one-day delay later in the trial.
The court was expected to finalise its jury selection and begin opening arguments on Tuesday, but was delayed by the request.
Mr Bannon is facing federal charges of contempt for defying a congressional subpoena to appear before the House of Representatives' January 6 investigation committee.
Tuesday's morning session involved debates over how much of Mr Bannon's discussions with the committee could be introduced as evidence.
Mr Bannon was indicted on two counts of criminal contempt of Congress in November for defying a subpoena that would have made him provide records and testimony to the committee.
Each count carries a minimum of 30 days prison, or as long as a year. A conviction would not compel him to provide evidence to the committee.
Mr Bannon said at the time that executive privilege prevented him from testifying during the committee's investigation.
But the panel has said the privilege does not apply to him, as he was not a White House staff member on the days leading up to the attack on the Capitol.
Quotes from January 6 committee hearings — in pictures
Mr Nichols ruled that Mr Bannon could not use executive privilege as a defence in his case.
He had previously ruled that elements of Mr Bannon's defence were irrelevant and could not be introduced in court.
David Schoen, a lawyer for Mr Bannon, told the judge that his client believed he was in a continuing negotiations with the January 6 committee and that he “believed the dates were malleable” as talks continued.
“Mr Bannon believed, right or wrong, that the date had been extended,” Mr Schoen said.
Lawyers for the government are expected to say his failure to appear before the committee was a matter of defiance and disrespect.
“On its face the subpoena demands compliance,” said assistant US attorney Amanda Vaughn.
Ms Vaughn said the government would prove “the defendant’s attempts to wilfully defy the subpoena".
AP contributed to this report