Black Lives Matter is calling on Gov. Newsom to replace Harris with another Black woman.
The activist organization joins the state's Legislative Black Caucus in pushing for two California congresswomen -- Rep. Karen Bass and Rep. Barbara Lee -- as candidates.
Black Lives Matter says it wants to ensure the organization has proper representation in the Senate and has started a petition.
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Following Harris' historic role in the Senate, "it just makes sense to continue a tradition, but particularly from the perspective of African-American women," said Los Angeles County Supervisor Mark Ridley-Thomas, part of a group of Black California lawmakers pushing Bass.
Harris will be sworn in as President-elect Joe Biden's vice president on Jan. 20, and it's not yet clear how soon before then she will give up her seat. Newsom has said he has no timeline to make an announcement.
"We are working through the cattle call of considerations," he told reporters last week. "I want to make sure it's inclusive, I want to make sure that we are considerate of people's points of view."
Harris, the daughter of immigrants from Jamaica and India, is one of just two Black women to ever serve in the Senate. Carol Moseley Braun, who represented Illinois from 1993-1999, is the other.
The Associated Press contributed to this report.