A day after winning a Supreme Court victory over President Trump, the Manhattan district attorney moved one step closer to obtaining some of the president’s financial records when a lower-court judge acted quickly to hear any final arguments from the president’s lawyers.
The federal judge in Manhattan who first presided over the dispute issued an order on Friday asking the lawyers and the district attorney, Cyrus R. Vance Jr., to inform him as to whether any further action was needed in light of the Supreme Court’s ruling.
The judge, Victor Marrero, has scheduled a hearing for Thursday, when the president’s lawyers are expected to continue to fight against turning over the records to Mr. Vance.
The order came sooner than expected and seemed to signal that the judge would move swiftly to try to resolve the matter. For nearly a year, Mr. Vance, a Democrat, has been locked in a legal battle with the president over access to the records.
Last August, Mr. Vance’s office subpoenaed Mr. Trump’s accounting firm for tax records in connection with an investigation into hush money paid to Stormy Daniels, an adult film actress who said she had an affair with Mr. Trump, an allegation he has denied. The office asked for returns and other financial records dating to 2011.
Lawyers for Mr. Trump sued to block the grand jury subpoena, saying that the president was immune from state criminal inquiries while in office, an argument that had never been tested in court. They said local investigations could distract the president from his duties and that Mr. Vance was motivated by political considerations.
The case made its way to the Supreme Court, and on Thursday, the court ruled, 7 to 2, against the president. Chief Justice John G. Roberts Jr. wrote that “no citizen, not even the president, is categorically above the common duty to produce evidence when called upon in a criminal proceeding.”
Chief Justice Roberts added, however, that Mr. Trump could still raise objections in court to the scope and relevance of the subpoena, potentially setting up hearings before Judge Marrero that could take weeks or longer.
After the ruling was announced, the White House press secretary, Kayleigh McEnany, said in a statement that further proceedings were required in the lower court in which Mr. Trump could “raise additional arguments, including constitutional protections, against this frivolous and politically motivated subpoena.”
A spokesman for Mr. Vance declined to comment on Judge Marrero’s order.
Even if Judge Marrero allows Mr. Vance’s office to obtain some or all of the president’s records, the documents would not soon — and might never — become public. As part of a secret grand jury investigation, they would remain sealed unless an indictment were handed up and they were introduced as evidence at a hearing or trial.
The president’s former lawyer and fixer, Michael D. Cohen, paid Ms. Daniels $130,000 to buy her silence during the 2016 presidential campaign and later pleaded guilty to federal campaign finance charges for his role in that deal and another hush-money 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 were broken when Mr. Trump and his company, the Trump Organization, reimbursed Mr. Cohen.
Initially, Mr. Vance’s investigation focused on whether senior executives at the company falsely accounted for the reimbursement as a legal expense to cover up the nature of the payment, according to people briefed on the matter. In New York, falsifying a business record can be a crime.
The state prosecutors did some initial digging, interviewing Mr. Cohen in prison, empaneling a grand jury to investigate and subpoenaing records from the Trump Organization and from potential witnesses.
But the investigation slowed while Mr. Vance’s office awaited the Supreme Court’s ruling on whether prosecutors could examine Mr. Trump’s financial records, the people briefed on the matter said.
If the office gains access to Mr. Trump’s taxes, the investigation could broaden beyond the possible falsification of records to include other potential financial crimes, one of the people added.
Little has been said publicly about the scope of Mr. Vance’s grand jury investigation. Late last year, in defending the subpoena before Judge Marrero, Mr. Vance’s office outlined the inquiry on two pages in a larger public court filing, but that section was redacted in its entirety.
The legal deadline has expired for bringing a misdemeanor charge of filing false business records. The office can bring a felony charge until about early 2022, five years after the Trump Organization reimbursed Mr. Cohen.
To prove a felony charge of falsifying records, Mr. Vance’s office would need to show not just that the records were falsified, but that it was done with the intent to defraud and to commit, or to conceal, another crime.
Toward that end, investigators could focus on possible tax crimes or on whether false information was provided to one of the Trump Organization’s banks.
Judge Marrero’s brief order on Friday offered no indication of how he might rule on final attempts by Mr. Trump to narrow or block the subpoena.
Last October, in a 75-page opinion, Judge Marrero rejected the president’s argument that he was immune from investigation, calling it “repugnant to the nation’s governmental structure and constitutional values.”