Manhattan prosecutors disputed many of Donald J. Trump’s arguments for delaying sentencing in his criminal hush-money case until after Election Day, but said they would leave the politically fraught decision to the judge alone.

In a letter to the judge overseeing the case, Justice Juan M. Merchan, prosecutors from the Manhattan district attorney’s office declined to endorse either the existing schedule or a delay. The former president had asked to postpone the sentencing until after the election partly so he had more time to challenge his conviction.

The sentencing is currently set for Sept. 18, just seven weeks before Election Day, when Mr. Trump, now a felon, will square off against Vice President Kamala Harris for the presidency. The prosecutors, the letter said, are “prepared to appear for sentencing” at any date the judge chooses.

“The people defer to the court on the appropriate post-trial schedule that allows for adequate time” for Mr. Trump to challenge his conviction, “while also pronouncing sentence without unreasonable delay,” the prosecutors wrote in the letter, dated Aug. 16 and released on Monday.

The district attorney, Alvin L. Bragg, appeared to strike a middle ground in hopes of navigating around a partisan backlash so close to Election Day.

If Mr. Bragg had opposed a postponement, Mr. Trump would have accused him of meddling in the election. But explicitly consenting to Mr. Trump’s delay tactics might have alienated Mr. Bragg’s liberal Manhattan base as it demands accountability for the former president, who was convicted in May of falsifying business records to conceal a sex scandal.

The decision now rests squarely in the hands of Justice Merchan, a no-nonsense veteran judge who has shown little patience for Mr. Trump’s many maneuvers to drag out the case. Justice Merchan has already postponed the sentencing once at Mr. Trump’s request, and might be hesitant to do so again.

Any delay past Election Day would be consequential. Voters would head to the polls knowing that Mr. Trump is a felon — a jury convicted him on all 34 felony counts — but not whether he will face time behind bars.

Mr. Trump faces up to four years in prison, though Justice Merchan could impose a shorter sentence or only probation.

Even if the judge grants a delay in sentencing, it could be brief. He might adjourn for only a couple weeks to provide Mr. Trump time to challenge his conviction, one reason the former president’s lawyers cited for needing a delay. Or he could hold the sentencing during the presidential transition period later this year.

If Mr. Trump wins the election, Justice Merchan could postpone any punishment to be served after Mr. Trump’s term in office expires. A sitting president cannot be prosecuted, let alone incarcerated. But Mr. Trump could not pardon himself in the Manhattan case, since the presidential pardon power does not extend to state crimes.

Mr. Trump’s attempt to reschedule the sentencing coincides with his recent political struggles. Ms. Harris’s entry into the presidential race a month ago has upended the campaign, and appears to have erased the former president’s lead in the polls.

In a letter filed with the judge last week, Mr. Trump’s lawyers implied that sentencing him just weeks before Election Day on Nov. 5 could improperly influence voters. The lawyers, Todd Blanche and Emil Bove, wrote that waiting to hold the sentencing until after the election would allow the court to “reduce, even if not eliminate, issues regarding the integrity of any future proceedings.”

They also argued that the current sentencing date could compromise Mr. Trump’s efforts to challenge his conviction, an effort that hinges on a recent ruling by the U.S. Supreme Court granting him broad immunity for official actions as president. Already, Mr. Trump’s lawyers have asked Justice Merchan to throw out the charges, citing the Supreme Court ruling, and the judge has promised to rule on that request on Sept. 16.

This is a developing story and will be updated.