Fani T. Willis, the district attorney prosecuting the Georgia election interference case against former President Donald J. Trump, acknowledged on Friday a “personal relationship” with a prosecutor she hired to manage the case but argued that it was not a reason to disqualify her or her office from it.

The admission came almost a month after allegations of an “improper, clandestine personal relationship” between the two surfaced in a motion from one of Mr. Trump’s co-defendants. The motion seeks to disqualify both prosecutors and Ms. Willis’s entire office from handling the case — an effort that, if successful, would likely sow chaos for an unprecedented state criminal prosecution of a former president.

“While the allegations raised in the various motions are salacious and garnered the media attention they were designed to obtain, none provide this Court with any basis upon which to order the relief they seek,” Ms. Willis’s filing said, adding that “the personal relationship between” Ms. Willis and the prosecutor, Nathan J. Wade, “has never involved direct or indirect financial benefit” to Ms. Willis.

Ms. Willis’s filing includes an affidavit from Mr. Wade asserting that the personal relationship started only after Mr. Wade had been hired.

The original motion containing the accusations, filed by Michael Roman, a former Trump campaign official, alleged that Ms. Willis had hired her “boyfriend” as a special prosecutor, granting him lucrative contracts even though he was underqualified, and then benefited from going on vacations that Mr. Wade paid for.

But Ms. Willis said in her filing that “financial responsibility for personal travel taken is divided roughly evenly” and Mr. Wade echoed that language in his affidavit, adding that Ms. Willis “received no funds or personal financial gain from my position as Special Prosecutor.”

Mr. Roman’s motion also alleged that the relationship began before Mr. Wade started working for the Fulton County district attorney’s office in November 2021. But in her filing on Friday, Ms. Willis included an affidavit from Mr. Wade in which he stated that he had “developed a personal relationship” with Ms. Willis in 2022.

The allegations, and Ms. Willis’s silence about them until now, have thrown the high-stakes prosecution off balance, giving Mr. Trump a new line of attack and raising the prospect of delays or more serious impacts on the case. Ms. Willis has sought to have the trial start in August, but no date has been set.

This is a developing story. Check back for updates.