• Video report by ITV News Washington Correspondent Robert Moore

A post-mortem examination commissioned for George Floyd’s family found that he died of asphyxiation due to neck and back compression when a Minneapolis police officer held his knee on Mr Floyd’s neck for several minutes and ignored his cries of distress, the family’s lawyers have said.

The post-mortem found the compression cut off blood to Mr Floyd’s brain, and weight on his back made it hard to breathe, lawyer Ben Crump said at a news conference.

The family’s procedure differs from the official post-mortem as described in a criminal complaint against the officer.

That autopsy included the effects of being restrained, along with underlying health issues and potential intoxicants in Mr Floyd’s system, but also said it found nothing "to support a diagnosis of traumatic asphyxia or strangulation".

Mr Floyd, a black man who was in handcuffs at the time, died after the white officer ignored bystanders’ shouts to get off him and Mr Floyd’s cries that he couldn’t breathe.

George Floyd died while in police custody. Credit: AP

Speaking at a makeshift memorial for his brother, Mr Floyd said: "I understand y'all upset like it was already said, I doubt y'all are half as upset as I am. So if I'm not over here wilding out, if I'm not over here blowing up stuff, if I'm not over here messing up my community, then what are y'all doing?"

"What you are doing, y'all not doing nothing, because that's not gonna bring my brother back at all."

Terrence Floyd dropped to his knees when walking up to the memorial and prayed as chants of "George Floyd" from the crowd rang out.

He called on protestors to find another way to vent their outrage at his brother's death.

"In every case of police brutality, the same thing has been happening. Y'all, protest, you destroy stuff. And they don't move, you know why they don't move? Because it's not their stuff, it's our stuff. So they want us to destroy our stuff. They not going to move. So let's do this another way. Let's do this another way."

George Floyd's brother Terrance addressing the crowd at a makeshift memorial to him. Credit: AP

The latest comes as US president Donald Trump has called the nation’s governors "weak" and demanded tougher crackdowns on protesters railing at police killings of black people.

Mr Trump spoke to governors on a video teleconference with law enforcement and national security officials in the aftermath of another night of violent protests in dozens of US cities.

The president told local leaders they “have to get much tougher” after six days of unrest set off by the death of George Floyd, a black man who died after he was pinned at the neck by a white Minneapolis police officer.

"Most of you are weak," Mr Trump told governors, telling them to "arrest people."

The president had to take refuge in a White House bunker during angry scenes outside. Credit: AP

Mr Floyd's death, captured on citizen video, sparked days of protests in Minneapolis that have spread to cities around America.

The official post-mortem last week provided no other details about intoxicants, and toxicology results can take weeks.

In the emergency call that drew police, the caller described the man suspected of paying with counterfeit money as “awfully drunk and he’s not in control of himself”.

Mr Crump said last week that he was commissioning the family’s own post-mortem.

Mr Floyd’s family, like the families of other black men killed by police, wanted an independent look because they did not trust local authorities to produce an unbiased test.

Demonstrators in Washington are protesting against the death of George Floyd in police custody Credit: AP

The family’s post-mortem was conducted by Michael Baden and Allecia Wilson.

Mr Baden is the former chief medical examiner of New York City, who was hired to conduct a post-mortem of Eric Garner, a black man who died in 2014 after New York police placed him in a chokehold and he pleaded that he could not breathe.

Mr Baden also conducted an independent post-mortem of Michael Brown, an 18-year-old shot by police in Ferguson, Missouri. He said that procedure, requested by the teenager’s family, did not reveal signs of a struggle, casting doubt on a claim by police that a struggle between Mr Brown and the officer led to the shooting.

The officer who held his knee on Mr Floyd’s neck, Derek Chauvin, has been charged with third-degree murder and manslaughter and is in custody in a state prison.

Derek Chauvin has been charged with murder and manslaughter. Credit: Hennepin County Sheriff/AP

The other three officers on scene, like Chauvin, were fired the day after the incident but have not been charged.

Mr Crump on Monday called for the remaining three officers to be arrested and for the charge against Chauvin to be upgraded to first-degree murder.

The head of the Minneapolis police union said in a letter to members that the officers were fired without due process and lawyers are fighting for their jobs.

Lieutenant Bob Kroll, the union president, also criticised the city leadership, saying a lack of support is to blame for the days of sometimes violent protests.

Mayor Jacob Frey said: “For a man who complains so frequently about a lack of community trust and support for the police department, Bob Kroll remains shockingly indifferent to his role in undermining that trust and support.”

Mr Frey said Mr Kroll’s opposition to reform and lack of empathy for the community has undermined trust in the police.

State governor Tim Walz announced on Sunday that attorney general Keith Ellison would take the lead in any prosecutions in Mr Floyd’s death.

Local civil rights activists have said Hennepin County attorney Mike Freeman does not have the trust of the black community.

They have protested outside his house, and pressed him to charge the other three officers. He remains on the case.