President-elect Donald J. Trump on Tuesday intensified a last-minute effort to avoid his criminal sentencing in New York, urging an appeals court to intervene and halt the proceeding.

In a filing with the First Department of the state’s Appellate Division, Mr. Trump’s lawyers sought an emergency stay of the sentencing, which is scheduled for Friday, 10 days before his presidential inauguration. The lawyers argued that Mr. Trump was entitled to full immunity from prosecution, and even sentencing, now that he is the president-elect.

The sentencing, his lawyers, Todd Blanche and Emil Bove, wrote, “threatens irreparable harm and deprivation of President Trump’s constitutional rights.”

The lawyers also filed an action in the appeals court against the trial judge overseeing the case, Juan M. Merchan, challenging two of his recent decisions to uphold a New York jury’s verdict against Mr. Trump.

The filings marked an escalation of Mr. Trump’s long-running effort to fend off sentencing and unwind his conviction, to avoid becoming the first felon to occupy the Oval Office. Ever since the jury convicted him in May on 34 felony counts of falsifying records to cover up a sex scandal, Mr. Trump has attacked the verdict on various fronts, including demanding that Justice Merchan throw out the case.

This is a developing story and will be updated.