Memorial tributes to Floyd in Minneapolis, where he was killed on May 25, and in New York City's borough of Brooklyn - a major flashpoint for demonstrations - came as protesters returned to the streets of several US cities for a 10th-straight day, including Atlanta, Washington DC, Denver, Detroit and Los Angeles.

The gatherings, while boisterous at times, were for the most part orderly, in contrast to several previous nights punctuated by sporadic arson, looting and clashes between protesters and police.

The change in mood reflected a determination voiced by many protesters and organisers to transform outrage over Floyd's death into a renewed civil rights movement, seeking reforms to America's criminal justice system.

"This is a very seismic moment and, some day, I'm going to have a kid, and he or she or they are going to ask me what I did during the uprising of 2020, during the American spring," said Nana Mensah, a writer in her 30s from Brooklyn.

She held a sign reading: "You're lucky we just want equality and not revenge".

In the capital, hundreds if not thousands assembled for a rally at the Lincoln Memorial, many sitting on the ground listening to speakers and chanting, "Say his name - George Floyd".

Another group of protesters congregated near the White House, where workers had erected concrete barriers and fences.

Two Buffalo, New York, officers were suspended after a video showed them shoving a 75-year-old man to the ground as he approached police lines. The man was taken to hospital where he was in a stable but serious condition.

Delivering the eulogy at a memorial service inside a Minneapolis university chapel, Sharpton said Floyd's fate - dying at the hands of police, pinned to the ground under the knee of a white officer - symbolised a universal experience of police brutality for African Americans.

"George Floyd should not be among the deceased. He did not die of common health conditions. He died of a common American criminal justice malfunction," Sharpton said. "It's time for us to stand up in George's name and say, 'Get your knee off our necks'."

Sharpton led mourners in eight minutes and 46 seconds of silence, the amount of time Floyd lay on a Minneapolis street with a knee pressed into his neck.

In addition to hundreds who gathered inside the chapel, hundreds listened to the service over loudspeakers outside.

Zsa-Vona Williams, 36, knew Floyd from his days working at the homeless shelter where she once lived, recalling him as a caring, friendly soul.

"He gave to and fed a lot of people. He was a gentle, peaceful person," Williams said.

The prayer service, which drew comic actors Kevin Hart and Tiffany Haddish as well as US Senator Amy Klobuchar of Minnesota, coincided with a separate outdoor memorial tribute to Floyd in Brooklyn.

The day of remembrance capped more than a week of largely peaceful protests, accompanied by civil unrest which prompted dozens of cities to impose overnight curfews and the mobilisation of the National Guard in several states.

The size of disturbances seemed to ebb after prosecutors in Minneapolis on Wednesday elevated murder charges against the former policeman jailed last week over Floyd's death and arrested three others accused of aiding and abetting.

On Thursday, the three newly arrested officers made their first appearance in court and were ordered to remain held on $750,000 bond each.

Their principal co-defendant, Derek Chauvin, 44, is slated to appear on Monday for his bond hearing. Chauvin is the officer seen in video footage kneeling on Floyd's neck as Floyd gasped for air and groaned, "I can't breathe", before passing out.

The four ex-Minneapolis officers, all dismissed the day after Floyd died, each faces up to 40 years in prison if convicted of the most-serious charges.

Floyd's brother Terrence joined an outdoor memorial in Brooklyn where many in the crowd knelt in a symbol of protest and chanted, "No justice, no peace".

He urged the crowd to continue to seek justice but to avoid violence, saying, "My brother wasn't about that".

Mayor Bill de Blasio took the stage to pledge Floyd's death would lead to substantive changes in police practices in New York.

Memorial services for Floyd were expected to stretch across six days and three states. A funeral was planned for Tuesday.

Australian Associated Press