The special prosecutor leading the election interference case against former President Donald J. Trump will not have to testify this week about an alleged romantic relationship with his boss, Fani T. Willis, the Fulton County district attorney, after reaching a divorce settlement on Tuesday.

The resolution of the divorce between the special prosecutor, Nathan J. Wade, and his wife leaves unanswered, for the time being, a question that has created potential peril for Ms. Willis’s high-profile prosecution of Mr. Trump and 14 of his allies.

Ms. Willis hired Mr. Wade, a lawyer in private practice, in 2021 to help run the Trump case, saying that she needed a trustworthy confidant for the job. But a filing three weeks ago from one of Mr. Trump’s co-defendants, Michael Roman, claimed that the two prosecutors were romantically involved and had taken vacations paid for by Mr. Wade.

Mr. Roman argues that this amounts to a conflict of interest, and is grounds for removing both prosecutors, as well as Ms. Willis’s entire office, from the case.

So far, neither Mr. Wade nor Ms. Willis have confirmed or denied the allegations of a relationship. But in recent days, it seemed increasingly likely that Mr. Wade would be forced to address the claims at a divorce hearing on Wednesday, where he was expected to take the stand.

The hearing was scuttled at the last minute, with a “temporary agreement” announced by the judge on Tuesday afternoon. Mr. Wade married Joycelyn Wade in 1997 and filed for divorce more than two years ago.