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.

A divide emerged last spring as the presidents of several universities, including Harvard and Columbia, adopted cautious responses when confronted by House Republicans at congressional hearings regarding antisemitism. In contrast, K-12 leaders, including David C. Banks, chancellor of New York City’s public schools at the time, took a combative approach.

The latest wave of pushback is spreading. In Chicago, Mayor Brandon Johnson, a Democrat, told reporters on Friday that the city would take the Trump administration to court if it snatched away funding, according to The Chicago Tribune.

“We’re not going to be intimidated by these threats,” Mr. Johnson said. “It’s just that simple. So whatever it is that this tyrant is trying to do to this city, we’re going to fight back.”

Unlike universities that rely on federal funding for medical and scientific research, public school districts are more insulated from threats to their bottom line because 90 percent of their funding comes from state and local taxes.

The Trump administration’s memo used a broad interpretation of a Supreme Court decision in 2023 that declared race-based affirmative action programs were unlawful at colleges and universities. That ruling did not address issues involving K-12 schools.

The expansive reasoning did not sit well with New York. The state’s letter argued that the case did “not have the totemic significance that you have assigned it” — and that federal officials were free to make policy pronouncements, but “cannot conflate policy with law.”

Mr. Morton-Bentley also called out what he described as an about-face within the top ranks of the administration.

He pointed out that the education secretary in President Trump’s first term, Betsy DeVos, once told staff that “diversity and inclusion are the cornerstones of high organizational performance.” She also said that “diversity and inclusion are key elements for success” for “building strong teams,” he wrote.

“This is an abrupt shift,” Mr. Morton-Bentley said, adding that the federal government has “provided no explanation for how and why it changed positions.”

The Trump administration’s memo included a certification letter confirming compliance that officials must sign and return to the Education Department within 10 days. New York indicated that it would treat the demand as a request rather than a requirement.

“No further certification will be forthcoming,” the state’s letter said.