The Manhattan district attorney’s office suggested on Monday that it had been investigating President Trump and his company for possible bank and insurance fraud, a significantly broader inquiry than the prosecutors have acknowledged in the past.

The suggestion by the office of the district attorney, Cyrus R. Vance Jr., came in a new federal court filing arguing that Mr. Trump’s accountants should have to comply with a grand jury subpoena seeking eight years of his personal and corporate tax returns. Mr. Trump has asked a judge to declare the subpoena invalid.

Until now, the district attorney’s inquiry had appeared largely focused on hush-money payments made in the run-up to the 2016 presidential election to two women who said they had affairs with Mr. Trump.

In the new filing, the prosecutors did not explicitly identify the matters under scrutiny in the grand jury inquiry, which by law is conducted in secret. But they said that “undisputed” assertions in earlier court papers and several news reports about Mr. Trump’s business practices showed that the office had a wide legal basis for the subpoena.

“In light of these public reports of possibly extensive and protracted criminal conduct at the Trump Organization,” there was nothing improper or even unusual about the subpoena, the filing said.

The prosecutors cited newspaper reports, including one that concluded the president may have illegally inflated his net worth and the value of his properties to lenders and insurers. They also included an article on the congressional testimony of his former lawyer and fixer, Michael D. Cohen, who told lawmakers last year that the president had committed insurance fraud. Lawyers for the president have denied wrongdoing.

The suggestion that the investigation, which has gone on for nearly two years, was broader than Mr. Vance’s office had previously acknowledged could raise the stakes for Mr. Trump, his company and its executives, if the inquiry were ever to lead to charges of bank or insurance fraud, which are felonies.

The inquiry into the hush-money payments seemed to center on a less serious crime, the filing of false business records.

A spokesman for Mr. Vance’s office declined to comment. Lawyers for Mr. Trump did not reply to requests for comment.

Asked about the investigation at a White House briefing, Mr. Trump called it a “continuation of the worst witch hunt in American history.”

“It’s a terrible thing that they do,” Mr. Trump said, referring to Democrats. “It’s really a terrible thing.”

Mr. Trump and Mr. Vance have been locked in battle over the subpoena for almost a year in a case that already has gone to the Supreme Court. The district attorney’s office has said that fight has slowed the investigation, and it remains unclear how much work prosecutors have been able to do in the interim or whether charges are likely to result.

It is also unknown whether prosecutors are investigating other possible crimes that were not suggested in the new filing.

Rebecca Roiphe, a former assistant district attorney in Manhattan who now teaches at New York Law School, said Mr. Vance’s decision to cite public accusations of wrongdoing allowed his office to defend its subpoena without revealing the actual focus of its investigation.

“They could be going on a totally different tangent,” Professor Roiphe said. “The prosecutor is just doing what he has to do in order to suggest this is a broad white-collar investigation, which generally justifies fairly broad subpoenas to financial institutions.”

Mr. Vance, a Democrat, subpoenaed Mr. Trump’s accounting firm, Mazars USA, in August 2019 for the tax returns and other financial records dating to 2011. Mr. Trump tried to block the subpoena almost immediately, initially arguing that as a sitting president, he was immune from state criminal investigation.

The case wound its way through the federal courts until last month, when the Supreme Court soundly rejected that argument in a major ruling on the limits of presidential power. The decision cleared the way for prosecutors to seek Mr. Trump’s financial records, but the court also said Mr. Trump could return to the lower court in Manhattan, where he first sued to stop the subpoena, and raise new objections.

Mr. Trump’s lawyers argued last week that the subpoena was overbroad and politically motivated, asking the federal judge, Victor Marrero, to block it and declare it unenforceable.

Mr. Vance’s office responded with the filing on Monday, contending that Mr. Trump’s argument “rests on the false premise that the grand jury’s investigation is limited to so-called ‘hush-money’ payments” made by Mr. Cohen in 2016.

“This court is already aware that this assertion is fatally undermined by undisputed information in the public record,” the prosecutors wrote, before citing the media accounts.

Mr. Cohen had arranged payments to the adult film star Stormy Daniels and another woman, Karen McDougal, a former Playboy model. Mr. Vance’s office has been looking into whether any New York State laws were broken when those payments were made.

Mr. Cohen, who pleaded guilty to federal campaign finance violations for his role in the payments, is serving a three-year prison sentence in home confinement in his apartment in Manhattan. Federal prosectors concluded their investigation into the matter last year and have not charged anyone else.

In a recent federal court hearing, Mr. Vance’s office accused Mr. Trump of dragging out the legal fight in order to effectively shield himself from criminal investigation.

“What the president’s lawyers are seeking here is delay,” Carey R. Dunne, a lawyer in Mr. Vance’s office, told Judge Marrero.

Mr. Dunne said that the longer Mr. Trump fought the case, the greater the chance that the statute of limitations would expire for any potential crimes that might have been committed, effectively granting the president immunity.

“Let’s not let delay kill this case,” Mr. Dunne argued.

Jay Sekulow, a lawyer for the president, denied after the hearing that Mr. Trump’s lawyers were pursing a strategy of delay. “Our strategy seeks due process,” Mr. Sekulow said in an email at the time.

If Mr. Vance succeeds in eventually obtaining Mr. Trump’s records, they are unlikely to become public anytime soon because they will be shielded by grand jury secrecy rules. The records might only emerge later if criminal charges are brought and the records are introduced in a trial.