The family of George Floyd, the African-American man whose death in Minneapolis police custody triggered nationwide violent protests, joined a diverse crowd of nearly 60,000 people and marched peacefully through the streets of downtown Houston to pay tribute to him.

Floyd, who died after a Minneapolis police officer pressed his knee into his neck for several minutes, grew up in Houston, Texas.

From rappers to pastors to politicians, the diverse crowd heard from emotional speakers at the march held to pay homage to Floyd.

Chanting "hands up, don't shoot" and "no justice, no peace", the crowd, estimated to be over 60,000, along with 16 members of Floyd's family, some of whom flew down to Houston, marched about a mile from Discovery Green Park to City Hall under the scorching sun.

But when the sun went down, things took a slight turn.

Around 7 pm, several water bottles were thrown. Police then moved in on the crowd near Avienda de las Americas and made several arrests, many of which were for blocking roadways, Khou11.Com reported.

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.

Organised by rappers Trae Tha Truth and Bun B, the march had as its participants several city leaders and officials, including Mayor Sylvester Turner, Congresswoman Sheila Jackson Lee, Lizzie Fletcher and Sylvia Garcia, and Congressman Al Green.

Before beginning the march to City Hall, Rapper Bun B asked the crowd to kneel for 30 seconds of silence in memory of George Floyd, the report said.

"We gonna sweat today. ... But we ain't gonna shed a drop of blood in Houston, Texas," the rapper said, calling for a peaceful protest.

Houston Police Chief Art Acevedo and other police officers expressed solidarity by kneeling with the marchers.

Lakewood Church Pastor Joel Osteen led a prayer with Floyd's family members, with the crowd later getting down on one knee and observing silence for 30 seconds in the memory of the Houston man.

"Never did I think we would have this many people for my brother,” said Floyd's sibling, while a nephew of his said, "don't stop until we get justice for my uncle."

Rapper Bun B led the chanting crowd. He said "What's his name?" and the crowd replied, "George Floyd." "That's right and do not you ever forget it," Bun B said.

Reverend Bill Lawson, who had marched with Dr Martin Luther King, addressed the marchers and said "(the crowd) needs to make noise". "We have been quiet for too long," he said.

Mayor Turner said that as "we protest and demonstrate, we do it in such a way that we do not deface George Floyd's name".

"This day is not about City Hall. This is your city. Today is about the family of George Floyd," Turner said.

"We want them to know that George did not die in vain," the mayor said addressing the rally.

"Let me say to his family, as the mayor of the fourth largest city, that we are with you in the years to come. George Floyd did not die in vain. We are not perfect. We recognise that. In our city, we respect every person, every person is important, every neighbourhood is of value. We have to commit ourselves to doing better every day," Turner said.

Congresswoman Lee said, "I want us to know the pain of these loved ones ... Some of whom I've had police officers tell me what an inspiration George Floyd was. You are this nation. And I've come here to take your nation (back)".

It is time for a revolution of change, she said.

Congressman Green said he is angry because not only do "we want an arrest, we want a conviction."

It is time to declare a war on racism in the United States, he said, adding that US President Donald Trump should have been impeached for his racism.

Before the event, officials urged those marching to have their voices heard, while demonstrating peacefully.

Shortly before the start of the march, the City of Houston in an alert asked the public to report any suspicious behaviour.

Houston Public Works crews have removed several piles of bricks and rocks from locations around the city, officials said.

The protests across the country have led to the death of at least five persons, arrest of over 4,000 people and damage to property worth billions of dollars.