The district attorney leading a criminal case against Donald J. Trump and his allies in Georgia accused Representative Jim Jordan of Ohio of trying to obstruct her prosecution of the case in a sharply worded letter she sent on Thursday.

Soon after the district attorney, Fani T. Willis, a Democrat, announced last month that she was bringing a racketeering case against Mr. Trump and 18 other defendants for their efforts to overturn the results of the 2020 presidential election in Georgia, Mr. Jordan, a Republican and chairman of the House Judiciary Committee, said that he was going to investigate Ms. Willis over whether her prosecution of Mr. Trump was politically motivated.

In her letter, Ms. Willis accused Mr. Jordan of trying “to obstruct a Georgia criminal proceeding and to advance outrageous partisan misrepresentations,” and of not understanding how the state’s racketeering law works.

“Your attempt to invoke congressional authority to intrude upon and interfere with an active criminal case in Georgia is flagrantly at odds with the Constitution,” she added. “The defendants in this case have been charged under state law with committing state crimes. There is absolutely no support for Congress purporting to second guess or somehow supervise an ongoing Georgia criminal investigation and prosecution.”

The letter came as the defendants and the prosecution continued sparring in legal filings over where and when the trial would take place. In a new filing, Mark Meadows, a defendant, who served as the White House chief of staff under Mr. Trump, was seeking a stay of the proceedings in state court until a judge ruled on his motion to move his case to federal court.

The Georgia case is one of four criminal indictments that have been brought against Mr. Trump this year; Mr. Jordan’s investigation of Ms. Willis is the latest example of House Republicans using their power in Congress to try to derail efforts to prosecute the former president.

When he announced his inquiry last month, Mr. Jordan, a close Trump ally, said it would look for any evidence of communication between Ms. Willis and the Biden administration and examine her office’s use of federal grant money.

While Mr. Jordan expressed concerns that former federal officials were being unfairly targeted in a state prosecution, some of the issues he raised had little to do with the underlying facts of the investigation. For example, in a letter to Ms. Willis, he said her new campaign website had included a reference to a New York Times article that mentioned the Trump investigation.

Ms. Willis’s response is the latest sign that she will not take attacks on her office and the investigation quietly — a striking difference in style from that of Jack Smith, the more reserved and laconic special prosecutor handling the two federal criminal cases against Mr. Trump.

She has a track record as a pugnacious, law-and-order prosecutor, and is pursuing racketeering cases not only against the former president and his allies, but a number of high-profile Atlanta rappers accused of operating a criminal gang.

In a heated email exchange in July over the terms of Gov. Brian Kemp, a Republican, providing testimony in her investigation, Ms. Willis called the governor’s lawyer, Brian McEvoy, “wrong and confused” and “rude,” among other things.

“You have taken my kindness as weakness,” she wrote, adding: “Despite your disdain this investigation continues and will not be derailed by anyone’s antics.”

In her letter to Mr. Jordan, she invited him to purchase a book about racketeering statutes written by one her fellow prosecutors on the Trump case, John Floyd, titled “RICO State by State.”

“As a non-member of the bar,” she wrote, “you can purchase a copy for two hundred forty-nine dollars.”