President-elect Donald J. Trump’s latest attempt to stave off his criminal sentencing in New York was denied on Monday, teeing up a frenzied series of last-minute appeals as his inauguration draws near.

The denial came from the trial judge overseeing the case, Juan M. Merchan, who scheduled the sentencing for Friday, 10 days before Mr. Trump is scheduled to be sworn in for a second presidential term.

Although Mr. Trump’s lawyers had implored the judge to postpone the sentencing, Justice Merchan dismissed their claims as “a repetition of the arguments he has raised numerous times in the past.”

Mr. Trump is now poised to escalate his effort, court filings show, turning to a New York appeals court in hopes that it will intervene in his case.

Late Monday, Mr. Trump’s lawyers filed a civil proceeding against Justice Merchan before the appeals court, challenging two of the judge’s recent decisions to uphold Mr. Trump’s conviction. Mr. Trump’s lawyers will argue to the appeals court that Mr. Trump is immune from criminal prosecution now that he is the president-elect.

The flurry of filings demonstrates the great lengths to which Mr. Trump will go to avoid his sentencing.