A bipartisan group of 35 former federal judges on Wednesday asked the judge who oversaw President Trump’s remarkable lawsuit against the Internal Revenue Service to reopen the case and conduct an inquiry into whether the hasty deal to resolve it could be challenged as an act of fraud.

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......

At the heart of the former judges’ argument was an assertion that Mr. Trump improperly used his lawsuit against the I.R.S. as a way to obtain “unlawful private benefits” for himself and his family and to create a fund that would dole out taxpayer money “without constitutional or congressional authority.” Moreover, the former judges claimed that the president tried to shield the deal from “judicial scrutiny” by “short-circuiting” Judge Williams’ ability to examine its terms.....

Acknowledging that her hands were tied, Judge Williams quickly closed the case, but noted in her order that there had never been a “settlement of record.” Within hours, however, the terms of a deal surfaced in public in an agreement that was signed by a senior Justice Department official and detailed how the fund would work. The next day, the department released an addendum to the agreement giving the Trump family its own extraordinary boon: immunity from all past I.R.S. investigations.

In their court papers, the former judges laid out that sequence of events, telling Judge Williams that it showed the fraudulent nature of the agreement. The judges said she did not have to rule immediately that settlement was invalid, suggesting that she could first “commence an inquiry into the whether the court was deceived.”