Senator Mitch McConnell, the minority leader, led Republican senators on Friday in protesting a proposed Biden administration rule promoting education programs that address systemic racism and the legacy of American slavery, calling the guidance “divisive nonsense.”

In a letter to Education Secretary Miguel Cardona, Mr. McConnell, of Kentucky, and three dozen other Republicans singled out a reference in the proposal to The New York Times Magazine’s 1619 Project, which was included as an example of a growing emphasis on teaching “the consequences of slavery, and the significant contributions of Black Americans to our society.”

“Families did not ask for this divisive nonsense. Voters did not vote for it,” the senators wrote. “Americans never decided our children should be taught that our country is inherently evil.”

It was the latest bid by Republicans to stoke outrage within their conservative base about President Biden’s agenda, which party leaders are increasingly portraying as a radical overreach into every corner of American life.

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With Mr. Biden pushing a number of popular domestic programs, Republicans have increasingly turned to litigating cultural issues to attack him and his party, accusing them of advancing a divisive agenda focused on political correctness, a message they believe will help them regain majorities in both the House and the Senate in 2022.

In his official party rebuttal to Mr. Biden’s address to a joint session of Congress on Wednesday night, Senator Tim Scott of South Carolina, the lone Black Republican, upbraided Democrats, colleges and corporations for “doubling down” on the nation’s racial divisions “by pretending we haven’t made any progress at all.”

“Kids again are being taught that the color of their skin defines them, and if they look a certain way, they’re an oppressor,” Mr. Scott said, adding later: “Hear me clearly: America is not a racist country.”