Floyd, a black man who died after a white officer pressed his knee into Floyd's neck for minutes, even after he stopped moving, grew up in Houston and a public memorial and burial is planned there for next week.
Protesters marched from a downtown Houston park to City Hall where, at a rally that lasted a little over an hour, various local and congressional officials, activists and members of Floyd's family spoke.
People march in honor of George Floyd on June 2, 2020 in Houston, Texas. Members of George Floyd's family participated in a march that went from Discovery Green to City Hall with support from the local chapter of Black Lives Matter. (Photo by Sergio Flores/Getty Images)
Mayor Sylvester Turner told the crowd that the rally and march were about "lifting up the family of George Floyd."
"Today we want to love on them. We want them to know that George did not die in vain," he said.
Turner said about 16 members of Floyd's family participated in the march and rally.
Several members of Floyd's family spoke at the rally, telling protesters of their appreciation for their support and asking them to not be violent in any protests in which they participated.
Members of George Floyd's family participated in a march that went from Discovery Green to Houston City Hall with support from the local chapter of Black Lives Matter. (Photo by Sergio Flores/Getty Images)
Before the start of the Houston march, Houston rapper Bun B, who organized the event with fellow Houston rapper Trae Tha Truth, told the crowd the march and rally would be peaceful and he asked the crowd to look out for anybody who could cause trouble.
Bun B then led the crowd of at least several thousand on a chant as he said "What's his name?" and the crowd replied, "George Floyd."
"That's right and don't you ever forget it," Bun B said.
Police officers lined the route of the march and large city dump trucks blocked some downtown streets. Afterward, Police Chief Art Acevedo told the crowd to not let violence hijack their peaceful protests.
"God as my witness, change is coming," Acevedo said regarding the impact of Floyd's death. "And we're going to do it the right way."
Former President George W. Bush criticized any effort to squelch protests of George Floyd's death while in Minneapolis police custody.
In a statement issued Tuesday by his office in Dallas, the former Republican president said he and wife Laura Bush "are anguished by the brutal suffocation of George Floyd and disturbed by the injustice and fear that suffocate our country."
"It is a strength when protesters, protected by responsible law enforcement, march for a better future. … Those who set out to silence those voices do not understand the meaning of America - or how it becomes a better place," he said.
More than 3,000 state troopers have been assigned across Texas to bolster local law enforcement amid the protests.
Since Friday, there have been nearly 880 arrests during protests in Dallas, according to police and the county sheriff's office.
Of those, 674 people were arrested Monday during a largely peaceful protest that police ended after the group marched onto a bridge. The protesters in that mass arrest were charged with obstructing a roadway but released without being sent to jail, police spokeswoman Tamika Dameron said.
Dallas officials expanded a 7 p.m.-6 a.m. curfew zone Tuesday to include the bridge where the Monday night mass arrest happened. No expiration date has been set for the curfew, which covers central Dallas and some adjoining neighborhoods.
Austin Police say a 20-year-old black protester was critically injured after being struck by a beanbag fired by a police officer. Police Chief Brian Manley says the officer had been aiming at another demonstrator but missed.
(© Copyright 2020 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)