New York prosecutors on Thursday urged the U.S. Supreme Court to deny President-elect Donald J. Trump’s last-ditch effort to halt his criminal sentencing, in a prelude to a much-anticipated ruling that will determine whether he enters the White House as a felon.

In a filing a day before the scheduled sentencing, prosecutors from the Manhattan district attorney’s office called Mr. Trump’s emergency application to the Supreme Court premature, saying that he had not yet exhausted his appeals in state court. They noted that the judge overseeing the case plans to spare Mr. Trump jail time, which they argued undermined any need for a stay.

The prosecutors, who had secured Mr. Trump’s conviction last year on charges that he falsified records to cover up a sex scandal that endangered his 2016 presidential campaign, implored the Supreme Court to let Mr. Trump’s sentencing proceed.

“There is a compelling public interest in proceeding to sentencing,” they wrote, and added that “the sanctity of a jury verdict and the deference that must be accorded to it are bedrock principles in our Nation’s jurisprudence.”

The district attorney’s office has so far prevailed in New York’s appellate courts, but Mr. Trump’s fate now rests in the hands of a friendlier audience: a Supreme Court with a 6-to-3 conservative majority that includes three justices Mr. Trump appointed. Five are needed to grant a stay.

Their decision, coming little more than a week before the inauguration, will test the influence Mr. Trump wields over a court that has previously appeared sympathetic to his legal troubles.

In July, the court granted former presidents broad immunity for official acts, stymying a federal criminal case against Mr. Trump for trying to overturn the 2020 election. (After Mr. Trump won the 2024 election, prosecutors shut down that case.)

The revelation that Mr. Trump spoke this week by phone with one of the conservative justices, Samuel A. Alito Jr., has fueled concerns that he has undue sway over the court.

Justice Alito said he was delivering a job reference for a former law clerk whom Mr. Trump was considering for a government position. But the disclosure alarmed ethics groups and raised questions about why a president-elect would personally handle such a routine reference check.

It is unclear whether Justice Alito will recuse himself from the decision, which the court could issue promptly.

Mr. Trump’s sentencing is scheduled to begin at 9:30 a.m. Friday in the same Lower Manhattan courtroom where his trial took place last spring, when the jury convicted him on all 34 felony counts.

If the Supreme Court rescues Mr. Trump on Thursday, returning him to the White House on Jan. 20 without the finality of being sentenced, it will confirm to many Americans that he is above the law. Almost any other defendant would have been sentenced by now.

“A sentencing hearing more than seven months after a guilty verdict is aberrational in New York criminal prosecutions for its delay, not its haste,” the prosecutors wrote.

The prosecutors also noted that Mr. Trump would most likely avoid any punishment at sentencing. The trial judge, Juan M. Merchan, has signaled he plans to show Mr. Trump leniency, reflecting the practical impossibility of incarcerating a president.

Still, Mr. Trump’s lawyers argued that the sentencing could impinge on his presidential duties. It would formalize Mr. Trump’s conviction, cementing his status as the first felon to occupy the Oval Office.

That status, Mr. Trump’s lawyers wrote in the filing to the Supreme Court, would raise “the specter of other possible restrictions on liberty, such as travel, reporting requirements, registration, probationary requirements and others.”

The court’s immunity ruling also underpinned Mr. Trump’s request to halt his sentencing. In the application, Mr. Trump’s lawyers argued that he was entitled to full immunity from prosecution — as well as sentencing — because he won the election.

“This court should enter an immediate stay of further proceedings in the New York trial court,” the application said, “to prevent grave injustice and harm to the institution of the presidency and the operations of the federal government.”

Mr. Trump’s application was filed by two of his picks for top jobs in the Justice Department: Todd Blanche, Mr. Trump’s choice for deputy attorney general, and D. John Sauer, his selection for solicitor general.

“Forcing President Trump to prepare for a criminal sentencing in a felony case while he is preparing to lead the free world as president of the United States in less than two weeks imposes an intolerable, unconstitutional burden on him that undermines these vital national interests,” they wrote.

Whether that argument will prevail is uncertain. Some legal experts have doubted the merits of Mr. Trump’s application, and lower courts have greeted his arguments with skepticism.

Earlier Thursday, a judge on the New York Court of Appeals in Albany, the state’s highest court, declined to grant a separate request from Mr. Trump to freeze the sentencing.

Prosecutors noted that Mr. Trump had yet to have a full appellate panel rule on the matter, and that he had not mounted a formal appeal of his conviction. Consequently, they argued, the Supreme Court “lacks jurisdiction over this non-final state criminal proceeding.”

Also this week, a judge on the First Department of New York’s Appellate Divison in Manhattan rejected the same request to halt the sentencing.

That judge, Ellen Gesmer, grilled Mr. Trump’s lawyer at a hearing about whether he had found “any support for a notion that presidential immunity extends to president-elects?”

With no example to offer, Mr. Blanche conceded, “There has never been a case like this before.”

In their filing Thursday, prosecutors echoed Justice Gesmer’s concerns, noting that “This extraordinary immunity claim is unsupported by any decision from any court.”

They also argued that Mr. Trump’s claims of presidential immunity fell short because their case concerned a personal crisis that predated his first presidential term. The evidence, they said, centered on “unofficial conduct having no connection to any presidential function.”

The state’s case centered on a sex scandal involving the porn star Stormy Daniels, who threatened to go public about an encounter with Mr. Trump, a salacious story that could have derailed his 2016 campaign.

To bury the story, Mr. Trump’s fixer, Michael D. Cohen, negotiated a $130,000 hush-money deal with Ms. Daniels.

Mr. Trump eventually repaid him. But Mr. Cohen, who was the star witness during the trial, said that Mr. Trump orchestrated a scheme to falsify records and hide the true purpose of the reimbursement.

Although Mr. Trump initially faced sentencing in July, his lawyers buried Justice Merchan in a flurry of filings that prompted one delay after another. Last week, Justice Merchan put a stop to the delays and scheduled the sentencing for Friday.

Mr. Trump faced four years in prison, but his election victory ensured that time behind bars was not a viable option. Instead, Justice Merchan indicated that he would impose a so-called unconditional discharge, a rare and lenient alternative to jail or probation.

“The trial court has taken extraordinary steps to minimize any burdens on defendant,” the prosecutors wrote Thursday.