Prosecutors with the Manhattan district attorney's office said Tuesday they would oppose President-elect Trump's attempt to dismiss his criminal hush money conviction in New York -- but they told the judge they do not object to pausing the case.

The DA's office faced a Tuesday deadline to propose the next steps in the case after the "unprecedented circumstances" of the former president's election following his conviction on 34 felony counts earlier this year.

Trump's sentencing in the criminal case is tentatively scheduled for Nov. 26, though defense attorneys have asked New York Judge Juan Merchan to dismiss the case ahead of Trump's impending inauguration.

Trump's lawyers laid out their new argument to dismiss the case in a filing made public Tuesday, writing that the case must be dismissed because a sitting president is immune from prosecution.

"To require President Trump to address further criminal proceedings at this point would not only violate the federal Constitution, but also disrupt the Presidential transition process," wrote defense lawyers Todd Blanche and Emil Bove, both of whom Trump nominated last week to top DOJ posts in his new administration.

Prosecutors pushed back on that claim, arguing that presidential immunity would not apply to a defendant who had already been convicted for conduct that is entirely private.

The district attorney's office instead suggested deferring all remaining proceedings in the case, including the Nov. 26 sentencing, until after Trump leaves the White House in 2029.

"The People deeply respect the Office of the President, are mindful of the demands and obligations of the presidency, and acknowledge that Defendant's inauguration will raise unprecedented legal questions. We also deeply respect the fundamental role of the jury in our constitutional system," prosecutors wrote.

Defense lawyers argued that, while Trump is not yet president, presidential immunity equally applies during the transition process and added that their appeal of the case would "take a year or more" and possibly reach the Supreme Court, dragging the case well past Inauguration Day.

"There is no material difference between President Trump's current status after his overwhelming victory in the national election and that of a sitting President following inauguration," their filing said.

Judge Merchan will have the final say regarding the next steps in the case.

Since July, Trump's attorneys have been pushing to have the conviction vacated and the case dismissed by arguing that prosecutors filled "glaring holes in their case" with evidence of official acts that the Supreme Court recently ruled off limits in its landmark presidential immunity decision.

Trump's lawyers have also argued for a dismissal by citing the Presidential Transition Act of 1963, which urges government officers to take "lawful steps to avoid or minimize disruptions" to the presidential transition.

Prosecutors have argued that the Supreme Court's ruling that Trump is entitled to immunity from criminal prosecution for official acts undertaken while in office has no bearing on Trump's conviction.

"The People agree that these are unprecedented circumstances," prosecutor Matthew Colangelo told the court last week.

Trump was convicted in May of all 34 felony counts of falsifying business records related to a hush money payment to adult film actress Stormy Daniels to silence allegations about a 2006 sexual encounter with Trump in order to boost his electoral prospects in the 2016 presidential election.

His conviction carries a maximum penalty of up to four years in prison, but first-time offenders would normally receive a lesser sentence.