ATLANTA — Coming out of their debate in a key center of black America, the leading Democratic presidential contenders aimed for the party’s crucial black and minority vote, with the scramble putting internal party tensions on display.

From black protesters disrupting Elizabeth Warren to the lone black woman in the race chiding white, upstart Mayor Pete Buttigieg, the dynamics in Atlanta highlighted the push for crucial black and other minority support with less than three months before primary voting begins. They further underscored some candidates’ vulnerabilities in trying to assemble the coalition necessary to win the nomination — and defeat President Donald Trump in the general election.

Warren electrified a raucous and racially diverse crowd in the Clark-Atlanta University gymnasium as she tries to expand her support beyond the white liberal base that boosted her in the primary polls this summer. But the Massachusetts senator had to endure protests of a black school-choice group that threatened to overshadow her message aimed squarely at black women — Democrats’ most loyal faction.

Buttigieg, the South Bend, Indiana, mayor who leads caucus polls in overwhelmingly white Iowa, spent the day defending remarks relating his experience as a gay man to the systemic racism facing African Americans. Kamala Harris, the California senator and only black woman in the race, blasted his approach as “naive.”

Like Buttigieg, Bernie Sanders invoked his biography, as the child of an immigrant family with casualties in the Holocaust, to connect with African Americans’ struggle against oppression and white supremacy. Harris, still lagging the front-runners, has not criticized the way Sanders talks about race, but the Vermont senator still must prove he can get more black votes than he did in losing the 2016 nominating fight.