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Mr. Henderson said that despite deep divides on Capitol Hill, his coalition has not encountered opposition to their bid to link the 1963 march for jobs and economic freedom to an array of modern issues.

“We may have come from different places … but we’re all in the same boat now,” he said, evoking a quote in which King referred to coming from “different ships” before uniting in solidarity.

They have found a natural bridge in the late Bayard Rustin, an openly gay black man who served as a chief architect of the 1963 march but remained on the sidelines at the main event. Mr. Obama recently decided to award Rustin, who died in 1987, the Medal of Freedom.

The White House said “Mr. Rustin stood at the intersection of several of the fights for equal rights.”

That intersection is on display in the march’s host city, where the District’s Democratic politicians championed the rights of same-sex couples and immigrants for years before Saturday’s event.

D.C. Mayor Vincent C. Gray, a 70-year-old Democrat and city native, attended the 1963 march and has applied lessons from the civil rights movement to the city’s fight for full voting rights in Congress.

“The mayor pointed out that Dr. King himself addressed this: ‘Injustice anywhere is a threat to justice everywhere,’” Gray spokesman Pedro Ribeiro said. “We have a duty to confront all injustice, whether it’s the treatment of immigrants, discrimination against our LGBT friends and family, or the lack of representation for D.C. residents.”

Dick Gregory, a comedian and key civil rights era figure, said in an interview that the array of social movements in play now were spawned by the civil rights movement, when “the whole atmosphere around the world changed because of the underdog winning a victory.”

But there is a significant difference between the once-in-a-lifetime march of 1963 and Saturday’s festivities.

“Ain’t nobody scared,” he said, noting the vast number of black Americans who feared being stopped by police in their travels to Washington decades ago.

In that sense, he said, “it could never be compared at all.”