WASHINGTON—California Sen. Kamala Harris said Monday she will seek the Democratic nomination for president, launching a campaign to become the nation’s first woman and second African-American to win the White House.

Ms. Harris, who served as San Francisco district attorney and California attorney general before being elected to the Senate in 2016, made her announcement in a Martin Luther King Jr. Day interview on ABC’s “Good Morning America” and in a video distributed to supporters.

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