The Manhattan district attorney’s office accused President Trump on Thursday of purposely dragging out a court battle over a subpoena seeking eight years of his tax returns in an attempt to effectively shield himself from criminal investigation.

Carey R. Dunne, a lawyer for the prosecutor’s office, told a federal judge that the longer the president disputes the subpoena, the higher the chance that the statute of limitations would expire for any possible crime that may have been committed.

The office is seeking the president’s personal tax returns and those of his family business, the Trump Organization, as part of an investigation into hush-money payments made in the run-up to the 2016 election. The president has been fighting the subpoena for nearly a year.

“What the president’s lawyers are seeking here is delay,” Mr. Dunne said. “I think that’s the entire strategy here.”

He added: “Let’s not let delay kill this case.”

The prosecutor’s assertion came during a virtual hearing held before the judge, Victor Marrero, of Federal District Court in Manhattan. Mr. Trump’s lawyers did not respond directly to the accusation in court.

Jay Sekulow, a lawyer for Mr. Trump, said later in an email, “Our strategy seeks due process.”

The district attorney, Cyrus R. Vance Jr., a Democrat, issued the subpoena to Mr. Trump’s accounting firm, Mazars USA, in August.

Mr. Trump initially fought the subpoena last year with a bold and untested argument: that a sitting president was immune from a state criminal investigation. Judge Marrero oversaw that case and ruled against the president, and his decision was upheld by an appeals court.

The case went to the Supreme Court, which last week also rejected the president’s argument. Still, the high court left open the possibility that Mr. Trump could raise new objections to the subpoena.

The case was sent back to Judge Marrero, who called for the hearing this week so that both sides could outline their positions.

At the hearing, a lawyer for the president, William S. Consovoy, made it clear that Mr. Trump was likely to raise challenges to the scope of the subpoena, which Mr. Consovoy characterized as “widely overbroad,” and to raise the question of whether there was a political motivation in issuing it.

After the Supreme Court ruling was handed down last week, the White House press secretary, Kayleigh McEnany, called the subpoena “frivolous and politically motivated.”

Mr. Consovoy also said the president should be able to learn more about the district attorney’s investigation, which largely has been kept secret, and suggested that it was unfair for him to have to challenge a subpoena without having access to “at least some information about its nature and scope.”

At the hearing, Judge Marrero noted that in his ruling last year rejecting the president’s claim of immunity, he also found that the district attorney was not acting in bad faith.

In arguing that the delay could prevent a grand jury from considering evidence before any statutes of limitations ran out, Mr. Dunne said that the president was effectively getting the immunity from criminal inquiry that the Supreme Court denied him. Other people and entities could also escape scrutiny, Mr. Dunne said, without elaboration.

Mr. Trump’s lawyers must outline their new objections to the subpoena by July 27, and Mr. Vance can then respond.

Mr. Vance has been looking into hush-money payments that Michael D. Cohen, the president’s lawyer and former fixer, made in 2016 to Stormy Daniels, an adult film actress who said she had an affair with Mr. Trump. The president has denied an affair.

Mr. Cohen later pleaded guilty to federal campaign finance violations for his role in that deal and another payment. Mr. Cohen, who is serving a three-year sentence at a federal prison in Otisville, N.Y., implicated the president, saying in court that he had acted on Mr. Trump’s orders.

After federal prosecutors concluded their investigation last year, Mr. Vance’s office began examining whether New York State laws had been broken when Mr. Trump and his company reimbursed Mr. Cohen. The subpoena was issued as part of that inquiry.

Even if Mr. Vance’s office wins its fight for the president’s records, the documents are not likely to become public in the foreseeable future. The materials would be shielded by grand jury secrecy rules and would probably emerge only if charges were later filed and the records were introduced as evidence at a trial.

Ben Protess contributed reporting.