Lawyers for President-elect Donald Trump on Wednesday demanded the immediate dismissal of his New York hush money conviction as the judge weighs whether to impose a sentence as planned, delay proceedings or toss out the case completely.

Attorney Todd Blanche, whom Mr. Trump has nominated for a top post at the Department of Justice, said the “nation’s people issued a mandate that supersedes the political motivations” of Democratic Manhattan District Alvin Bragg and “the people,” as prosecutors are known in court.

“Just as a sitting president is completely immune from any criminal process, so too is President Trump as president-elect,” Mr. Blanche wrote in a pre-motion letter to state Supreme Court Judge Juan Merchan. “This case must immediately be dismissed.”

Mr. Blanche plans to submit a full motion to dismiss the case by Dec. 20. His letter is a response to the position Mr. Bragg took on Tuesday — that a delay in Mr. Trump’s Nov. 26 sentencing is warranted, given the presidential transition, but a dismissal of the conviction is not.

Mr. Blanche said the Constitution’s Supremacy Clause is triggered and federal law must overtake Mr. Bragg’s local priorities. He also pointed to special counsel Jack Smith’s work to wind down his federal prosecutions of Mr. Trump before the inauguration.

“As in those cases, dismissal is necessary here,” Mr. Blanche wrote.

Mr. Trump is scheduled to be sentenced on Nov. 26, after a jury in May convicted him on 34 counts related to hush money payments near the 2016 election.

But Mr. Trump’s election victory threw the case into turmoil. Mr. Bragg does not want to drop the case but assented to a postponement of proceedings, perhaps until after Mr. Trump’s term ends in 2029.

The situation makes a pre-Thanksgiving sentencing unlikely. Instead, attorneys are poised to volley a series of motions through December about whether the case should be dismissed.

Judge Merchan also must decide whether Mr. Trump’s conviction should be nullified because of a U.S. Supreme Court decision that granted presidential immunity for official acts.

Defense attorneys say prosecutors used tweets and other evidence from Mr. Trump’s time in office in 2017 that should not have been considered by the jury.

The New York court is grappling with a precedent that dictates sitting presidents are not subject to criminal prosecution. Mr. Smith is winding down federal prosecutions of Mr. Trump for that reason.

Mr. Trump has already been convicted, however, making it an unusual situation.

At trial, prosecutors said Mr. Trump criminally concealed a hush-money payment to adult film star Stormy Daniels around the 2016 campaign with an intent to violate election laws.

They said Mr. Trump paid Ms. Daniels through his then-lawyer, Michael Cohen, and concealed reimbursements to the lawyer in 2017 by misidentifying checks.

Mr. Trump’s lawyers said he was busy running the country and thought he was paying Mr. Cohen for legal services, so his team logged the checks in that manner. They also said the trial was politically motivated and designed to thwart Mr. Trump’s presidential campaign.

Mr. Trump’s status as a convicted felon did not prevent him from easily defeating Vice President Kamala Harris on Election Day.

Earlier this month, Mr. Trump said he planned to nominate Mr. Blanche as deputy U.S. attorney general and one of his trial attorneys, Emil Bove, as principal associate deputy attorney general.