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.”