Video report by ITV News Correspondent Amy Lewis
The service – the first in a series of memorials in three cities over six days – took place in Minneapolis as a judge in the city set bail at 750,000 dollars (£600,000) for the three fired police officers charged with aiding and abetting murder in Mr Floyd's death.
Mr Floyd died on May 25 after a white police officer, Derek Chauvin, put his knee on the 46-year-old’s neck for several minutes as he lay handcuffed on the pavement.
Chauvin has been charged with murder, and he and the others could get up to 40 years in prison.
Reverend Al Sharpton delivered a eulogy at the North Central University in which he said: “George Floyd’s story has been the story of black folks.
“Because ever since 401 years ago, the reason we could never be who we wanted and dreamed to be is you kept your knee on our neck.
“It’s time for us to stand up in George’s name and say, ‘Get your knee off our necks!’”
Across the world, the video of Mr Floyd’s slow death has set off turbulent and sometimes violent demonstrations against police brutality, racism and inequality.
Those gathered at the Minneapolis tribute stood in silence for 8 minutes, 46 seconds, the amount of time Mr Floyd was alleged to be on the ground under the control of police.
Rev Sharpton vowed that this will become a movement to “change the whole system of justice”.
The service was also attended by the Reverend Jesse Jackson, Senator Amy Klobuchar, T.I., Ludacris, Tyrese Gibson, Kevin Hart, Tiffany Haddish and Marsai Martin.
Mr Floyd’s brother Philonise Floyd told the crowd about their childhood playing catch and eating banana and mayonnaise sandwiches.
He said: “All these people came to see my brother.
“That’s amazing to me that he touched so many people’s hearts because he touched our hearts.”
The casket was covered in red roses, and a vibrant image was projected above the pulpit of a mural of Mr Floyd painted at the street corner where he was arrested by police on suspicion of attempting to pay with a counterfeit note.
The message on the mural reads: “I can breathe now”.
In the US, where protests had been marked by bouts of lawlessness since last week, relative quiet prevailed for a third straight night on Thursday, a day after prosecutors charged the three other officers at the scene and filed a new, more serious count of murder against Chauvin.
In New York City, a large crowd gathered at Brooklyn’s Cadman Plaza and chanted “You are not alone” in a rally with another of George Floyd’s brothers.
“I thank God for you all showing love to my brother,” said an emotional Terrence Floyd.