“Given the immense power of the special counsel’s office and the costs to Mr. Papadopoulos of continuing to fight, he will serve his sentence tomorrow, and hopes to move on with his life,” Mr. LaVigne wrote in a statement.

Judge Moss dismissed a suggestion by Mr. Papadopoulos that his prison time should be delayed pending the resolution of a challenge to the appointment of the special counsel, Robert S. Mueller III, who is leading the investigation into Russian interference and whether there were any connections to the Trump campaign.

Lower courts have affirmed the validity of Mr. Mueller’s appointment.

Mr. Papadopoulos had suggested that the appeal could theoretically find Mr. Mueller’s appointment unlawful, and that, in turn, would result in his own conviction being set aside.

Judge Moss, however, said in the opinion on Sunday that Mr. Papadopoulos did not show that the appeal was likely to find Mr. Mueller’s appointment unlawful and, even if it did, such a finding was not likely to provide any new evidence that could set aside his conviction.

He also rejected what he characterized as Mr. Papadopolous’s “11th hour” request, filed on Nov. 21, to delay his sentence until he could further appeal any decision about the Mueller case.