A coalition of 19 states sued the Trump administration on Friday over its threat to withhold federal funding from states and districts with certain diversity programs in their public schools.

The lawsuit was filed in federal court by the attorneys general in California, New York, Illinois, Minnesota and other Democratic-leaning states, who argue that the Trump administration’s demand is illegal.

The lawsuit centers on an April 3 memo the Trump administration sent to states, requiring them to certify that they do not use certain diversity, equity and inclusion programs that the administration has said are illegal.

States that did not certify risked losing federal funding for low-income students.

Rob Bonta, the California attorney general, said at a news conference on Friday that the Trump administration had distorted federal civil rights law to force states to abandon legal diversity programs.

“California hasn’t and won’t capitulate. Our sister states won’t capitulate,” Mr. Bonta said, adding that the Trump administration’s D.E.I. order was vague and impractical to enforce, and that D.E.I. programs are “entirely legal” under civil rights law.

The Trump administration did not immediately respond to a request for comment on Friday evening.

The administration has argued that certain diversity programs in schools violate federal civil rights law, which prohibits discrimination on the basis of race, color and national origin in programs that receive federal funding.

It has based its argument on the Supreme Court’s 2023 ruling ending the use of race in college admissions, arguing that the decision applies to the use of race in education more broadly.

The administration has not offered a specific list of D.E.I. initiatives it deems illegal. But it has suggested that efforts to provide targeted academic support or counseling to specific groups of students amount to illegal segregation. And it has argued that lessons on concepts such as white privilege or structural racism, which posits that racism is embedded in social institutions, are discriminatory.

The lawsuit came a day after the Trump administration was ordered to pause any enforcement of its April 3 memo, in separate federal lawsuits brought by teachers’ unions and the N.A.A.C.P., among others.

Mr. Bonta said that the lawsuit by the 19 states brought forward separate claims and represented the “strong and unique interest” of states to ensure that billions of federal dollars appropriated by Congress reach students.

“We have different claims that we think are very strong claims,” he said.

Loss of federal funding would be catastrophic for students, said Letitia James, the attorney general of New York, an adversary of President Trump who previously won a civil fraud case against him.

She noted that school districts in Buffalo and Rochester rely on federal funds for nearly 20 percent of their revenue and said she was suing to “uphold our nation’s civil rights laws and protect our schools and the students who rely on them.”