TOPEKA, Kan. — Sixty years after the Supreme Court outlawed “separate but equal” schools for blacks and whites, civil rights advocates say American schools are becoming increasingly segregated, while the first lady, Michelle Obama, lamented that “many young people are going to schools with kids who look just like them.”

“Today, by some measures, our schools are as segregated as they were back when Dr. King gave his final speech,” Mrs. Obama told 1,200 graduating high school seniors Friday here in the city that gave rise to the landmark Brown v. Board of Education case.

In a speech that was part commencement address, part policy pronouncement and part journey into her own past, Mrs. Obama said that Brown’s advances were being reversed. “Many districts in this country have actually pulled back on efforts to integrate their schools, and many communities have become less diverse,” she said, leading to schools that are less diverse.

“And too often,” Mrs. Obama said, “those schools aren’t equal, especially ones attended by students of color which too often lag behind.”