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."
Mr Chauvin, who is shown in bystander footage appearing to kneel on Mr Floyd's neck for nearly eight minutes, replies: "Then stop talking, stop yelling.
"It takes heck of a lot of oxygen to talk."
The transcripts show Mr Floyd appears co-operative at the beginning of the arrest, repeatedly apologising to the officers after they approach his parked car.
Mr Lane asks Mr Floyd to show his hands at least 10 times before ordering him to get out of the vehicle.
In response to one of the demands to see his hands, Mr Floyd says: "Man, I got, I got shot the same way, Mr Officer, before." It is not clear what he is referring to.
At one point Mr Lane says: "Why's he getting all squirrelly and not showing us his hands and just being all weird like that?"
The officers then handcuff Mr Floyd and try to put him into the back of their police car. As they do, Mr Floyd becomes agitated, repeatedly pleading that he is claustrophobic.
Mr Lane asks if he is "on something". Mr Floyd replies: "I'm scared, man."
According to another document, Mr Lane told investigators that once in the car, Mr Floyd began "thrashing back and forth".
When asked "So he pushed himself out of the car?" Mr Lane replied: "Yeah".
The investigator then asks: "Versus you guys pulling him out of the car?" and Mr Lane says: "Yeah, because the goal is to keep him in the car, we didn't want him coming out again."
Pinned on the ground, according to the transcript, Mr Floyd cries out a dozen times: "Mama."
He says: "Can't believe this, man. Mom, love you. Love you.
"Tell my kids I love them. I'm dead."
At one point, when Mr Floyd continues to plead he can't breathe, Mr Lane asks Mr Chauvin: "Should we roll him on his side?"
Mr Chauvin responds: "No, he's staying put where we got him."
Mr Lane then says: "Okay. Just worry about the excited delirium or whatever."
Mr Chauvin replies: "Well that's why we got the ambulance coming," and Mr Lane says "Okay, I suppose".