"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.
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.
Clinton lamented that because of the recent killings of black people by police, Oliphant had to weep rather than simply feel the joys of being a child.
"Can you imagine? Nine years old -- she should be thinking about happy adventures, dreaming about all the wonderful things that her future holds for her," Clinton said. "Instead, she is talking about graveyards."
In the middle of Clinton's remarks in North Carolina, Oliphant took the stage and stood next to Clinton, beaming as the Democratic nominee hugged her.
It was in striking contrast to the image of Oliphant that the country became familiar with last week
With tears streaming down her face, the distressed girl said at a heated city council meeting: "It's a shame that our fathers and mothers are killed and we can't see them anymore."
"It's a shame that we have to go to their graveyard and bury them. And we have tears," she said. "We shouldn't have tears. We need our fathers and mothers to be by our side."
That city council meeting came on the heels of the death of Keith Lamont Scott.
A husband and father of seven children, Scott was shot and killed by police last month at an apartment complex. Police said they were looking for someone else with an outstanding warrant when Scott came out of a vehicle with a gun. But Scott's family has disputed that account, saying Scott was carrying a book.
Scott's death, along with the killing of Terence Crutcher by a police officer in Tulsa, Oklahoma, once again sparked national outrage, heated debates about the use of police force against minorities, as well as a series of protests.
Clinton had initially planned to visit Charlotte last Sunday, but scrapped those plans at the request of Charlotte Mayor Jennifer Roberts.
Clinton has made addressing systemic racism and police shootings a central part of her campaign, dedicating her first speech as a candidate to investing more in police departments in order to combat bias. During her remarks on Sunday, Clinton pledged to spur economic investment in impoverished areas, toughen gun laws and "build on the work that president Obama has done."
And while Clinton did not mention Republican nominee Donald Trump during in her remarks at church, she urged congregants to reject people who believe the way to fix implicit bias is more "law and order." Trump regularly calls himself the law and order candidate.
"Now, there are some out there who see this as a moment to fan the flames of resentment and division, who want to exploit people's fears, even though it means tearing our nation even further apart," Clinton said. "They say that all of our problems will be solved by simply more law and order, as if the systemic racism plaguing our country doesn't exist."
"Being stronger together with this common vision means rejecting those forces that try to pit us against each other," she said.