More: The move by the former judges was one of an increasing number of legal efforts to attack the validity of the two extraordinary benefits that emerged from the agreement last week: a $1.8 billion fund that could compensate allies of Mr. Trump who claim they suffered "weaponization" at the hands of the federal government and the conferral of lucrative tax benefits on the president, his family and his businesses.

The motion by the former judges, filed in Federal District Court in Miami, was a direct appeal to Judge Kathleen M. Williams, who closed the I.R.S. case last week after Mr. Trump voluntarily dismissed his suit. It asked her to bring the matter back to life under a rule that permits her to set aside a judgment she had made and examine the terms of the deal that appeared to have been reached in a plan to avoid that sort of scrutiny.

"The purported settlement' that was publicly disclosed after this court dismissed this matter raises profound questions about the parties' candor toward the court and manipulation of the judicial system, which threatens to undermine confidence in the administration of justice," lawyers for the former judges wrote.