Story highlights Hillary Clinton spoke out against recent police shootings in Charlotte and other cities

The Democratic nominee called it a symptom of systematic racism

Charlotte, North Carolina (CNN) Hillary Clinton told a black congregation here Sunday morning that her own grandchildren will never feel the fear that many African-American children do because they are white and privileged.

"I am a grandmother and like every grandmother, I worry about the safety and security of my grandchildren. But my worries are not the same as black grandmothers, who have different and deeper fears about the world that their grandchildren face," Clinton said.

In her remarks, Clinton quoted 9-year-old Zianna Oliphant, who garnered national attention when she tearfully spoke about the recent police killings of African-Americans at a Charlotte City Council meeting last week.

Hillary Clinton stands with Zianna Oliphant, 9, while speaking at Little Rock AME Zion Church in Charlotte, on Sunday.

Clinton said she "wouldn't be able to stand it" if her own grandchildren ever felt the kind of fear and worry that Oliphant and others have expressed.

"But because my grandchildren are white, because they are the grandchildren of a former president and secretary of state -- let's be honest here: They won't face the kind of fear that we heard from the young children testifying before the city council," Clinton said.

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