In some cities there have also been riots, and a section of Seattle has been declared an "occupied protest."
A Minneapolis police officer who knelt on Floyd's neck for nearly nine minutes while arresting him, Derek Chauvin, was fired by the department and has since been charged with second-degree murder and second-degree manslaughter in Floyd's death. Two other officers who knelt on Floyd, and one bystanding officer, have been charged with aiding and abetting second-degree murder and aiding and abetting second-degree manslaughter.
Amid the weeks of protest, both the Black Lives Matter movement and organization have gained increased national attention.
Now-retired Bishop Edward Braxton of Belleville, who is African-American, wrote a 2016 pastoral letter on the Catholic Church and the Black Lives Matter movement.
In that letter, Braxton said the Black Lives Matter movement doesn't have one leader or organizer.
"The phrase is more a call to action against racial profiling, police brutality, and racial injustice than a specific organization. The media and the public often associate a variety of unconnected groups with Black Lives Matter, when they are actually not structurally connected," the bishop noted.
However, Braxton noted that most leaders in the Black Lives Matter movement he had encountered reject the Church's teaching on sexuality, marriage and abortion.
Others in the movement, he said, are reluctant to work with the Church because they think Catholics have not done enough to fight racism, he wrote.
Braxton wrote that there are "profound differences" between the teachings of the Church and the Black Lives Matter movement, and that many leaders in that movement do "not embrace traditional Christian theological ideas about praying to keep the peace and change hearts."
"They embrace a radical theology of inclusion inspired by a revolutionary Jesus," he wrote.
The bishop nevertheless encouraged Catholic engagement with leaders of the Black Lives Matter movement.
Do differences "necessarily mean that a representative of the Church cannot have a meaningful conversation with representatives of the movement about these and other issues where there may be greater accord?" the bishop asked.
Braxton wrote that his dialogue with members of the movement had allowed him to present Church teaching on poverty and race, as well as on marriage, sexuality, and human dignity.
The bishop said that in dialogue, he "explained that the Church's social doctrine may be more forceful than they think. I also pointed out that Catholic beliefs about the nature of marriage, the meaning of human sexuality, and the dignity of human life from conception to natural death are not mere cultural norms or social issues. The Church cannot and will not change these moral doctrines. These beliefs represent what the Church firmly holds to be fundamental moral principles rooted in human nature, natural law, biblical revelation and the teachings of Jesus Christ."
Braxton wrote that all Catholics have an obligation to work for racial justice in the framework of Catholic teaching about the dignity of the human person, and the sanctity of human life, and to work, above all, for conversion.
"The Church has a grave responsibility to contribute to the ongoing conversion and spiritual transformation of us all. Working tirelessly day by day, we are co-workers with Christ."
Amid the ongoing protests, Bishop Fabre encouraged Catholics to take seriously the unique role they can play in promoting an end to racism.
The present moment, Fabre said, presents an "extraordinary opportunity" with many Americans taking an active part in protests against racism and police brutality. However, he said, the work still remains to be done "to dismantle racism."
"We should be seeking what unique role God might be asking the Catholic Church to play in transforming opportunity into a watershed moment in eradicating racism," he said.
African-American Catholics have suffered from racism within the Church for "decades and centuries," he said; sometimes it has taken the form of "parishes not welcoming the ministry of a black priest or deacon," he said, "or parishioners not wanting to receive the Eucharist from an African-American extraordinary minister of holy communion."
Black Catholics "long for the eradication of racism in the Church through encounter, accompaniment, repentance, justice, action, charity, and prayer," he said.