Former first lady Michelle ObamaMichelle LeVaughn Robinson ObamaJill Biden, Kate Middleton to meet this week Jill Biden to focus on military families on foreign trip Book claims Trump believed Democrats would replace Biden with Hillary Clinton or Michelle Obama in 2020 election MORE in a new interview is praising the Black Lives Matter movement and opening up about the concerns that she has for her two daughters.

In an interview on "CBS This Morning" that will air next Monday, Obama explained why she felt she needed to speak out after a Minneapolis jury found former police officer Derek Chauvin guilty in the murder of George Floyd last year.

Bystander footage that went viral showed Chauvin kneeling on Floyd’s neck for around nine minutes, ultimately resulting in Floyd’s death. Chauvin was found guilty of second-degree and third-degree murder and second-degree manslaughter last month.

The killing sparked months of demonstrations across the country last year, and a renewed discussion around race relations and police reform.

The Obamas issued a statement after the verdict, saying that the jury “did the right thing,” but that true justice “requires much more.”

Speaking to CBS’s Gayle KingGayle KingFauci to Chelsea Clinton: The 'phenomenal amount of hostility' I face is 'astounding' Caitlyn Jenner: My family not 'involved whatsoever' in gubernatorial bid 'CBS This Morning' moving to new Times Square studio MORE, Obama said despite the verdict, many in the Black community still feel certain anxieties.

“Many of us still live in fear as we go to the grocery store, or worry about our — walking our dogs, or allowing our children to get a license," she said.

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Obama also elaborated on the fears she has for her daughters, Malia and Sasha Obama.

“Every time they get in a car by themselves, I worry about what assumption is being made by somebody who doesn't know everything about them,” Obama said. “The fact that they are good students and polite girls. But maybe they're playin' their music a little loud. Maybe somebody sees the back of their head and makes an assumption.”

She added that those marching in support of Black Lives Matter are “takin' to the streets because they have to.”

“They're tryin' to have people understand that — that we're real folks,” Obama said. “And the fear that many have of so many of us is irrational. And it's based on a history that is just — it's sad, and it's dark. And it's time for us to move beyond that.”

Obama will appear on CBS to promote her Netflix Show “Waffles + Mochi,” which premiered in March.