Fran Davies, who is still in Pittsburgh with her husband, Les, said: 'We told her we loved her, that she was very brave and very special, but I think she already knew that.'
Mrs Davies, 29, told how she and Les, 43, had insisted to doctors that Laura 'was never to suffer, because sometimes, I think, children in hospitals suffer a little bit more than they need to'.
Laura had developed cancer-like growths as a side effect of the powerful anti-rejection drug she was being given which suppressed her immune system making it hard for her body to recognise abnormal cells.
Mrs Davies, plainly exhausted by the emotional ordeal of the past days, said: 'I could never live with myself if I felt she was suffering. I felt it was time, when she was starting to suffer.
'We didn't want Laura to die. We didn't want to lose Laura. I still don't want to lose her now. But what was happening to Laura and her body, the cancer was spreading and killing her . . . I didn't like what was happening to her. It wasn't going to give her quality of life. Laura was never going to be the Laura that she should have been.'
Mr Davies said: 'The decision we made was the right decision, before she started suffering really badly. I don't think she suffered at the end.'
Mrs Davies told of Laura's last moments with her 10-month-old brother, Ellis: 'She was stroking him and saying 'cheeky' and stuff. She loved the baby.'
She said the arrival of a new child in the middle of Laura's situation had been a lot to cope with. 'But I'm glad we did it and she had time to know him.'
Earlier, Laura's grandfather, Alan Cooper, interviewed on BBC 1's Good Morning programme from his home in Eccles, Greater Manchester, broke down as he described what he had heard of the little girl's last moments.
He said doctors had warned that, when her ventilator machine was turned off, Laura might gasp for breath: 'But when they did do it, she didn't. She just closed her eyes.'
Mr Cooper and his wife are currently looking after Ellis and his three-year-old brother, Louis, in Eccles. He told how Laura's constant cheerfulness and 'bubbling about' had always been a lift. 'She was a good inspiration to us all. It (her death) has not sunk in properly. I look at television programmes, seeing her running about - I can't believe it.'
The family rebutted criticism that prolonging Laura's life with such relatively untried surgery had caused her unnecessary suffering.
Mrs Davies said that perhaps in 10 years' time, such surgery would succeed. 'Unfortunately she was in a situation where things are still very experimental. But everything's experimental. If people don't try, how does anything ever advance?'
Mr Cooper declared: 'People that criticise have never been in the position of Fran and Les, and us as well. Unless you're in that position, and a lot of people out there have been . . . they know exactly what Fran and Les have been going through.'
Mr Cooper said he expected Mr and Mrs Davies back from Pittsburgh this weekend, or next week. He said a Manchester undertaker was getting in touch with the US authorities to arrange the return of Laura's body. A post-mortem examination was also being held, Mr Cooper said. 'Fran and Les agreed for this to be carried out to see if the doctors could learn anything from it.'Reuse content