NEW YORK — Donald Trump’s falsifying business records conviction should not be reversed because of the Supreme Court’s recent presidential immunity ruling for reasons including a wealth of incriminating evidence, prosecutors said in a court filing made public Thursday.

Manhattan District Attorney Alvin Bragg’s office wrote that the Supreme Court’s decision giving broad meaning to presidential immunity involving formal duties does not have any bearing on the May jury verdict that found Trump guilty on 34 felony counts for illegally trying to conceal the nature of a hush money payment to an adult-film actress shortly before the 2016 election.

Trump’s lawyers have argued that jurors were improperly exposed to witness testimony and records that were generated in 2017, his first year in office, that were extensions of the former president’s official duties. Prosecutors said the nation’s highest court did not hand down any finding that should disturb the verdict or see the case dismissed.

“The Supreme Court’s recent ruling thus has nothing to say about defendant’s conviction,’ lawyers for Bragg’s office wrote. “But even if that decision required the exclusion of all of the evidence that defendant cites here, there would still need be no basis for disturbing the verdict because of the other overwhelming evidence of defendant’s guilt.’

New York Supreme Court Justice Juan Merchan delayed Trump’s sentencing more than two months until Sept. 18 to give defense lawyers time to formally argue that evidence used by Bragg’s trial team was not admissible under the immunity doctrine which prohibits prosecution based on a president’s official acts.

The U.S. Supreme Court issued its controversial ruling July 1. The court ruled 6-3 along ideological lines that a president can’t face prosecution for official acts or through the use of evidence related to official conduct. Private conduct is not covered by that protection.

With the new timeline, the Republican presidential nominee could receive a jail sentence less than two months before the November election. He could also get a non-jail sentence or a sentence that is stayed pending the outcome of his appeal.

If Merchan upholds the verdict, the matter could be locked up in appeals until well after the election. An appeals court could stay enforcement of Trump’s sentencing.

Defense lawyers have argued that a significant amount of the evidence used against Trump at trial involved presidential actions and should have been excluded. The indictment should be dismissed altogether, they said, because the district attorney’s case has been intertwined with prohibited evidence since the case was presented to a grand jury last year.

The defense argued recently that Bragg’s office relied heavily “on official-acts evidence, including witness testimony regarding events in the Oval Office that [the prosecution] described as ‘devastating.’ ”

Bragg’s reply to Trump’s motion said “evidence that [Trump] claims is affected by the Supreme Court’s ruling constitutes only a sliver of the mountains of testimony and documentary proof that the jury considered in finding him guilty of all 34 felony charges beyond a reasonable doubt.”

A federal court judge has already ruled that Bragg’s case against Trump had nothing to do with his presidency. U.S. District Court Judge Alvin Hellerstein last year denied Trump’s bid to have the case transferred to federal court partially on that basis.

Separately, a New York civil judge on Thursday refused to step down from oversight of a wide-ranging business fraud case that resulted in a $450 million finding against Trump and his company. Judge Arthur Engoron defended himself against a claim by a lawyer not involved in the case, who told a news outlet that he had influence over Engoron.

Engoron wrote in his ruling that the attorney subjected him to a “90-second, unsolicited diatribe about a law” in the courthouse lobby and it had no impact on his bench trial verdict.