The unarmed black man cried out for his late mother and children as he said the Minneapolis policeman would kill him, transcripts from body-cam footage show.
They were disclosed in court by lawyers for one of the four officers involved.
The documents offer the clearest picture yet of Mr Floyd's last moments. His death in May sparked global uproar.
It led to a wave of anti-racism protests led by the Black Lives Matter movement, and stirred debate and reflection in the US over the country's history of slavery and segregation.
All four officers involved in taking Mr Floyd into custody were fired and arrested. Derek Chauvin, who knelt on his neck, faces several charges including second-degree murder, while the other three - Thomas Lane, J Alexander Kueng and Tou Thao - are charged with aiding and abetting murder.
The transcripts were made public on Thursday as Mr Lane's lawyers asked for the case against him to be dismissed.
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What do the transcripts show?
Until now, eyewitness footage shared on social media revealed most of what was known about Mr Floyd's arrest and his final moments.
The new transcripts give a more detailed account, shedding light on significant parts of the encounter, from the time Mr Lane and Mr Kueng arrived at the scene, to the point where Mr Floyd was given CPR in an ambulance.
Transcripts of footage recorded by body cameras fitted to Mr Lane and Mr Kueng show Mr Floyd said more than 20 times he could not breathe as he was restrained by the officers in a Minneapolis street.
They confronted him outside a convenience store where he was suspected of having used a forged $20 note to buy cigarettes.
At one point, a handcuffed Mr Floyd, while pinned down on the road next to the police car, gasps that he cannot breathe, adding: "You're going to kill me, man."
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