An Atlanta judge said on Monday that he would go forward with a hearing later this week delving into a romantic relationship between the two prosecutors leading an election interference case against former President Donald J. Trump and a number of his allies.

The revelations about the relationship, and accusations by defense lawyers that it has caused a conflict of interest, have created turmoil around the case. The defense is seeking to disqualify the two prosecutors — Fani T. Willis, the Fulton County district attorney, and Nathan J. Wade, who she hired to run the case.

“It’s clear that disqualification can occur if evidence is produced demonstrating an actual conflict or the appearance of one,” the judge, Scott McAfee of Fulton County Superior Court, said at a hearing on Monday afternoon.

He added that “because I think it’s possible that the facts alleged by the defendant could result in disqualification, I think an evidentiary hearing must occur to establish the record on those core allegations.”

This is a developing story. Check back for updates.