The New York State Education Department on Friday issued a defiant response to the Trump administration’s threats to pull federal funding from public schools over certain diversity, equity and inclusion programs, a remarkable departure from the conciliatory approach of other institutions in recent weeks.

Daniel Morton-Bentley, the deputy commissioner for legal affairs at the state education agency in New York, wrote in a letter to federal education officials that “we understand that the current administration seeks to censor anything it deems ‘diversity, equity & inclusion.’”

“But there are no federal or state laws prohibiting the principles of D.E.I.,” Mr. Morton-Bentley wrote, adding that the federal government has not defined what practices it believes violate civil rights protections.

The stern letter was sent one day after the federal government issued a memo to education officials across the nation, asking them to confirm the elimination of all programs it argues unfairly promote diversity, equity and inclusion. Title I funding for schools with high percentages of low-income students was at risk pending compliance, federal officials said.

New York’s stance differed from the muted and often deferential responses across academia and other major institutions to the Trump administration’s threats. Some universities have quietly scrubbed diversity websites and canceled events to comply with executive orders — and to avoid the ire of the White House.