Lawyers for President Trump said on Friday they would appeal a recent order from a judge casting doubt on the legitimacy of a $1.8 billion fund and extraordinary personal tax protections that emerged from a deal to drop his lawsuit against the Internal Revenue Service.

The notice of appeal, filed in Federal District Court in Miami, was the latest sign that Mr. Trump was willing to pursue his fight for the fund and the tax provision even though they have badly damaged his relations with Senate Republicans and jeopardized the confirmation of his pick for attorney general, Todd Blanche.

The move came at a moment of simmering tension between the White House and two Republican senators — John Cornyn of Texas and Thom Tillis of North Carolina — who have repeatedly vowed that they will not confirm Mr. Blanche unless he makes changes to the tax deal benefiting Mr. Trump and provides written assurances that the $1.8 billion fund to compensate his allies is dead once and for all.

On Thursday, Mr. Trump threw a wrench into the protracted negotiations between the senators and the Justice Department, threatening to withdraw Mr. Blanche’s name rather than give any ground to the demands by Mr. Cornyn and Mr. Tillis, who are not returning to Congress next year.

In a social media post on Friday, the president reiterated his support for the so-called anti-weaponization fund in particular, writing that the people it was intended to benefit — potentially including rioters who stormed the Capitol on Jan. 6, 2021 — still deserved restitution.

“Perhaps there has never been a group of people treated so badly in our Nation’s history,” he wrote. “They are suffering still, many ruined, and I felt that they should be given compensation for what has been done to them.”

The ruling by Judge Kathleen M. Williams, issued two weeks ago, was a repudiation of the secretive deal that ended Mr. Trump’s suit against the I.R.S., which originally demanded at least $10 billion in damages. The judge effectively accused the president and top officials at the Justice Department, including Mr. Blanche, of seeking to manipulate the court system to lend a veneer of validity to the backroom negotiations that had led to the creation of the fund and a sweeping provision to protect Mr. Trump, his family and his businesses from past tax inquiries.

Judge Williams issued her order at the request of 35 former federal judges who urged her to scrutinize the settlement of the suit as an act of fraud. A lawyer for the former judges, Norman L. Eisen, the chairman of Democracy Defenders Action, said the plan to appeal the decision proved that the concerns by Mr. Cornyn and Mr. Tillis were well-founded and that the president was still trying to keep the fund and the tax protections in place.

“This is the hill Trump has chosen to die on,” Mr. Eisen said.

The appeal would seek to lift Judge William’s finding that the underlying lawsuit — which accused the I.R.S. of failing to stop Mr. Trump’s tax returns from being leaked to the news media — was itself an improper exercise in self-dealing, given that he had brought the claim against a federal agency that he controlled.

If successful, it would also have a more practical effect: rolling back the judge’s efforts to seek disciplinary actions against Mr. Trump’s personal lawyers and Mr. Blanche and other department officials.

While Judge Williams described the deal in scathing terms, she acknowledged that she could not necessarily stop Mr. Blanche from establishing the $1.8 billion fund or giving the president immunity from audits.

“Whether executive branch actors can privately agree to give themselves and their former clients blanket immunities and billions of dollars in tax monies for legally undefined grievances was never an issue advanced to this court,” she wrote in her order.

Instead, it has been political pushback on Capitol Hill that has shaped the fate of the fund and audit deal. The fund was immediately politically toxic, even among Republicans, and Mr. Blanche has said that it is dead, though he has not formally put that commitment in writing.

The I.R.S. protections for the president and his family initially seemed to fly under the political radar for Republicans, until Mr. Cornyn and Mr. Tillis protested advancing Mr. Blanche’s nomination over the issue.

Mr. Cornyn and Mr. Tillis have both demanded that Mr. Blanche pare back the audit provision so that it only applies to Mr. Trump, two of his sons and the Trump Organization, rather than a potentially large pool of affiliates of the family. Mr. Cornyn also wants Mr. Blanche to include a provision making clear that Mr. Trump’s future tax return could still be audited.