Chief Justice John G. Roberts Jr. ruled on Monday that Peter Navarro, a trade adviser to Donald J. Trump during his presidency, must start serving a four-month sentence for contempt of Congress while he pursues an appeal.

The order will make Mr. Navarro, who refused to comply with a subpoena seeking information about the Jan. 6, 2021, attack on the Capitol, the first senior aide to Mr. Trump to serve time in connection with the plot to overturn the 2020 election. Mr. Navarro must report to a federal prison in Miami on Tuesday.

Chief Justice Roberts, acting on his own without referring the matter to the full Supreme Court, said he saw no reason to disagree with an appeals court’s determination that Mr. Navarro had not “met his burden to establish his entitlement to relief.”

The chief justice added that his order applied only to the question of whether Mr. Navarro should remain free while he appealed and did not express a view on the appeal itself.

A House committee had sought testimony and documents from Mr. Navarro about his plan to stall the certification of the election by holding up the counting of electoral votes. He refused to comply, saying that Mr. Trump had told him to invoke executive privilege.

After Mr. Navarro was convicted and sentenced, Judge Amit P. Mehta rejected his request to remain free while on appeal, saying there were no substantial legal questions for the courts to consider. The key point, wrote Judge Mehta, who was appointed by President Barack Obama, was that “the court found no evidence that President Trump ever invoked the privilege.”