The jury in the trial of the former Minneapolis police officer accused of murdering George Floyd retired today to begin its deliberations in the closely watched case.

Hennepin County Judge Peter Cahill issued final instructions to the jury after prosecutors and the defence attorney for Derek Chauvin made their closing arguments.

"You must be absolutely fair," Mr Cahill said. "Consider and weigh the evidence and apply the law."

In closing arguments earlier today, prosecutor Steve Schleicher said George Floyd pleaded for help with his "very last breath" but was not shown any compassion by Derek Chauvin.

"George Floyd begged until he could speak no more," Mr Schleicher told the jury in a Minneapolis courtroom. "All that was required was a little compassion and none was shown on that day."

"He asked for help with his very last breath but the officer did not help," Mr Schleicher said.

"He didn't follow training, he did not follow the department's use of force rules, he did not perform CPR," he said.

"George Floyd was not a threat to anyone, he was not trying to hurt anyone," Mr Schleicher said.

Mr Chauvin was seen on video kneeling on the neck of Mr Floyd as the 46-year-old African American lay facedown handcuffed on the ground for more than nine minutes.

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Mr Chauvin, 45, is charged with murder and manslaughter for Floyd's death on 25 May last year, which sparked protests across the United States and around the world against racial injustice and police brutality.

Mr Chauvin has pleaded not guilty to second-degree unintentional murder, third-degree "depraved mind" murder and second-degree manslaughter. He waived his right to testify before the jurors.

Mr Schleicher also told jurors to "believe your eyes" as he replayed video of Mr Floyd's death.

Over and over again, he repeated a phrase: "Nine minutes and 29 seconds," - the length of time Mr Chauvin was captured on video with his knee pressed into Mr Floyd's neck.

"This wasn't policing; this was murder," Mr Schleicher told jurors.

He cited the motto of the Minneapolis Police Department, which fired Mr Chauvin and three other officers involved the day after Mr Floyd's arrest: "To protect with courage and to serve with compassion."

"George Floyd was not a threat to anyone," Mr Schleicher said.

"Facing George Floyd that day that did not require one ounce of courage, and none was shown on that day, no courage was required. All that was required was a little compassion and none was shown on that day."

Afterwards, Mr Chauvin's lead lawyer, Eric Nelson, began his closing argument by emphasising and defining various abstract legal terms, including the presumption of innocence and proof beyond a reasonable doubt.

He said prosecutors were wrong to dismiss his theory that carbon monoxide poisoning from the nearby police car's exhaust fumes may have been a factor in Mr Floyd's death.

"Lawyers like to present evidence that favours them," Mr Nelson said.

The extensive video footage of Mr Floyd's death from multiple angles is a central part of the prosecution's case. Jurors have spent hours re-watching the videos played in the courtroom.

"Believe your eyes: what you saw, you saw,' Mr Schleicher said. "This case is exactly what you thought when you saw it first, when you saw that video. It is exactly that."

Mr Nelson argued that his client correctly followed the training he received over 19 years with the Minneapolis Police Department in dealing with a man as "large" as Mr Floyd.

Ahead of a verdict in Mr Chauvin's case, US National Guard troops have been deployed in the Minnesota city where shop windows have been boarded up as a precaution.

With tension high as a possible verdict nears, two guard members were slightly injured after at least one person opened fire from a car on a team of troops and police early yesterday in Minneapolis, authorities said.

Among the 38 witnesses who testified for the prosecution were some of the bystanders who watched Mr Floyd's arrest for allegedly using a counterfeit $20 note to buy a pack of cigarettes.

Darnella Frazier, the teenager who took the video that went viral, said Mr Floyd was "scared" and "begging for his life".

"It wasn't right. He was suffering," she said.

Much of the evidence phase of the trial involved testimony from medical experts about Mr Floyd's cause of death and whether Mr Chauvin had engaged in reasonable or excessive use of force.

A retired forensic pathologist put on the stand by the defence said Mr Floyd died of cardiac arrest brought on by heart disease and the illegal drugs fentanyl and methamphetamine.

Medical experts called by the prosecution said Mr Floyd died from hypoxia, or a lack of oxygen, from Mr Chauvin's knee on his neck and that drugs were not a factor.

The racially diverse jury is made up of six white women, three black men, three white men, two mixed race women and one black woman.

Three members of the jury will be excused by Judge Peter Cahill after closing arguments and the others will be sequestered for deliberations.

Three other former police officers, Tou Thao, Thomas Lane, and J Alexander Kueng, also face charges in connection with Mr Floyd's death.

They are to be tried separately later in the year.