The mother of schoolgirl Misbah Rana has offered to drop her claim for full custody of her daughter provided she has regular contact with her.
The 12-year-old, also known as Molly Campbell, left Scotland without her mother's consent last August to be with her father, Sajad Rana in Pakistan.
However, Louise Campbell's pursuit of an out-of-court settlement could be derailed by her daughter.
Misbah has told a news conference she does not wish to see her mother.
Lawyers for Ms Campbell, who lives in the Western Isles, has told the Supreme Court in Islamabad she would not insist on full custody in return for regular access to her daughter.
The court had been expected to make a ruling on whether Misbah should return to the UK.
Nahida Mahboob Elahi, Ms Campbell's lawyer, said the lengthy legal wrangling had made her client ill with stress.
Ms Elahi said: "I have made an offer on behalf of my client that she will not insist on full custody provided regular meetings with her daughter take place."
However, Misbah said she wishes to have nothing to do with her mother.
The girl said: "They say I have been abducted.
"This is not true. I am living with my father and I don't want to go to Britain."
Asked whether she would meet with her mother if she came to Pakistan, the girl said: "I don't want to see her."
She added: "I have my rights where I want to live and rights who I want to live with."
Ms Campbell issued a statement through her solicitors in Edinburgh.
She said: "I have fought very hard to have Molly returned to me because I believe that it would be best for her.
"She knows that I love her very much and that I will always be there for her. Everything I have done has been for Molly.
"However, after much soul searching and consideration of all the factors, I have now made proposals through my solicitor in Pakistan to Mr Rana."
Misbah's father Sajad Rana talks to media as he leaves court
Ms Elahi told the BBC of the effect the court proceedings have had on Ms Campbell's wellbeing.
She said: "She has said she is in a very bad state of health and it has caused a lot of mental and psychological strain fighting this battle."
Ms Elahi added: "She has not just dropped the custody case, she has just asked for an out-of-court settlement."
The Supreme Court has ruled that the parties involved should return next week with details of an out-of-court settlement and written details of how Misbah's estranged parents should get access to her.
Ms Campbell has intimated a wish that her daughter visit her in Scotland, although Mr Rana would prefer the visits to take place in Pakistan.
Another of the conditions tied into Ms Campbell's offer is that she be able to speak to her daughter by phone.
Mr Rana said Misbah was unable to attend the hearing in Islamabad because she was also unwell through stress.
In December, a hearing into Misbah's case was postponed until this month.
A judge sitting in Lahore High Court had ruled she be handed over to a female officer from the British High Commission by 6 December and then return to her mother.
He made his decision on the basis that the youngster was a UK resident and her case fell under its jurisdiction.
However, her return was delayed after Mr Rana appealed for Misbah to be allowed to stay in Pakistan while the custody case was resolved.
The case has drawn international attention since the youngster arrived in Lahore to live with her father and three siblings.