ATLANTA — One day after a televised debate featuring significant exchanges about race, Democratic presidential candidates fanned out across this capital of black political power to pitch their message to black voters and send a clear signal: Former Vice President Joseph R. Biden Jr. should not take support from African-Americans for granted.

Mr. Biden’s strength with black voters has been a key force in helping him maintain a polling edge in the race, even as the candidacies of Senators Elizabeth Warren of Massachusetts and Bernie Sanders of Vermont ascended among progressives. But on Thursday, both challengers — as well as Senators Kamala Harris and Cory Booker, two black candidates in the race, and other contenders — made explicit appeals about how they would address concerns and priorities of black voters.

Ms. Warren, who is Mr. Biden’s leading rival in many state and national polls, took direct aim at his reliance on black support by delivering one of her biggest speeches of the campaign, describing how governments and powerful corporations use racism and racial injustice as a wedge to divide working-class people. And she argued that it was time for the nation’s policies to include specific correctives to address discrimination.

“Don’t talk about race-neutral laws,” she said at a rally on Thursday evening at Clark Atlanta University, a historically black institution. “The federal government helped create the racial divide in this country through decades of active, state-sponsored discrimination, and that means the federal government has a responsibility to fix it.”