It was one of the odder tit-for-tat battles to have emerged so far in the federal case accusing former President Donald J. Trump of plotting to subvert the 2020 election.

Even though the proceeding was put on hold by Judge Tanya S. Chutkan while Mr. Trump seeks to have the charges tossed out with broad claims of immunity, prosecutors, trying to nudge it forward, have continued filing motions and turning over evidence. The former president’s lawyers have angrily accused them of violating the judge’s order and were eventually annoyed enough to ask that the prosecutors be held in contempt.

After simmering for a month, the dispute was resolved on Thursday when Judge Chutkan, who is handling the case in Federal District Court in Washington, issued an order saying she would not punish anyone with a finding of contempt.

Still, in what felt like an attempt to soothe the tensions between the defense and prosecution, the judge told both sides that they should not file any more “substantive” motions without first asking for permission.