Bill Cosby says he apologised to the family of the woman he is accused of drugging and assaulting only because her mother thought he was "a dirty old man", according to testimony read to the jury.

Cosby's explanation was contained in a deposition he gave over a decade ago as part of a lawsuit filed by Andrea Constand, the woman whose allegations resulted in the only criminal charges brought against the TV star.

Portions of the deposition became public nearly two years ago. For the jury at his sexual assault trial, this is likely to be the closest it comes to hearing from Cosby himself, since he has said he does not intend to take the stand.

In the deposition, he recounted a telephone conversation he had with Ms Constand's mother.

"I apologised to this woman. But my apology was, my God, I'm in trouble with these people because this is an old man and their young daughter and the mother sees this," he said in the 2005 deposition.

Ms Constand, 44, testified this week that Cosby penetrated her with his fingers against her will in 2004 after giving her pills that left her paralysed, unable to tell him to stop.

Cosby maintains the encounter at his Philadelphia home was consensual.

The 79-year-old TV star could spend the rest of his life in prison if convicted.

During the deposition, Cosby told lawyers that he knew his finances could suffer if the public was told he had drugged and assaulted someone.

"Do you think there would be a financial consequence to you if the public believed that you gave Andrea a drug that took away her ability to consent and then had sexual contact with her?" Cosby was asked.

"Yes," he said.

According to the deposition, Ms Constand's mother repeatedly asked Cosby over the phone about the pills he had given her daughter, but Cosby refused to tell her what they were and said he would send them in the mail, which he never did.

"I didn't want to talk about what did you give her. We're over the telephone and I'm not sending anything over the mail and I'm not giving away anything," Cosby testified.

Cosby also described calling Ms Constand's family and offering her money for graduate school.

Ms Constand refused the offer and reported Cosby to police, filing suit after prosecutors failed to file charges.

Cosby eventually settled with Ms Constand for an undisclosed sum, and his deposition was sealed for years, until a judge released parts of it in 2015.

The criminal case was reopened when Cosby's deposition became public.

In the deposition, Cosby said he gave Ms Constand three half-tablets of the cold and allergy medicine Benadryl before the "petting" began.

Prosecutors have suggested he drugged her with something stronger, perhaps quaaludes.

Friday's deposition excerpts were also expected to include an exchange where Cosby, once known as America's Dad, acknowledged using quaaludes, a now-banned sedative, in his pursuit of women for sex.

Some 60 women have come forward to say Cosby sexually violated them, but the statute of limitations for prosecution had run out in nearly every case.

Ms Constand's case is the only one in which Cosby has been charged.