The proposed rule involves a provision of the new Republican tax law that set a $10,000-a-year cap on deductions for state and local taxes. The cap helped Republicans keep the estimated cost of the tax law, which centers on a sharp reduction in the corporate tax rate, under $1.5 trillion, to comply with a budget procedure that allowed the bill to pass without the support of any Democrats.

Angered by the move, New York and New Jersey passed laws that set up charitable funds for state services, such as schools, and awarded state tax credits based on donations to those funds. Taxpayers making the donations would reduce their state taxes by the amount of the credit, but the state’s revenue would not fall. The idea was to create a roundabout way of funding state services that preserves a higher federal tax deduction for residents — because the charitable deduction is not subject to the same cap as the state and local tax deduction.

The Treasury rule would render those credits effectively useless for taxpayers. They would still be paying the same amount to the state, but receive no additional tax deduction from the federal government for their trouble.

Gov. Andrew Cuomo of New York, who has denounced the Republican tax law as “an economic missile” aimed at his state, threatened Thursday to take legal action against the proposed rule, calling it “an abuse of government power.”

More than 90 percent of households earning at least $200,000 in 2015 took the state and local deduction, writing off $269 billion in taxes, according to Internal Revenue Service data. Those households accounted for less than 5 percent of all filers in 2015, but took nearly 50 percent of the total deduction that year.