A woman at the center of a surrogacy fight who fled to Texas after the biological parents requested she have an abortion has asked the US supreme court to intervene so that she can keep the baby, who has a life-threatening heart defect.

McKenna West filed an emergency application on Wednesday asking the court to temporarily block a California court order recognizing the four-week-old child’s biological parents, Omar Ahmed and Nausheen Gilkar, as the legal parents.

The case rose to national attention in August when Ken Paxton, Texas’s attorney general, intervened in the dispute to ensure that the then unborn fetus received lifesaving medical treatment after birth for hypoplastic left heart syndrome, a rare congenital defect in which one side of the organ is underdeveloped, preventing normal blood flow.

Related: Baby with rare heart defect at center of surrogacy case in critical condition

The condition requires several surgeries to correct. Fewer than 1,000 babies each year are born with the condition, according to the Centers for Disease Control and Prevention. Without treatment, death can occur within days or weeks.

Paxton said the baby’s intended parents demanded that McKenna, the surrogate, terminate the pregnancy. But McKenna refused and travelled from Alaska to Texas, which bans most abortions, to seek sole conservatorship over the child. The biological parents, Gilkar and Ahmed of California, deny they forced West to have an abortion. Attorneys for Gilkar and Ahmed say West initially agreed to have the abortion.

The multistate custody dispute continued when a Texas judge ordered the hospital when the baby was born to provide lifesaving care and prohibited the child from being removed from Texas.

Gilkar and Ahmed, who named the child Rumi, obtained a restraining order barring West from seeing or holding the baby. They have not denied that they considered an abortion after learning of the fetus’s underdeveloped heart condition but say they later elected to continue the pregnancy.

Gilkar told the Dallas court during the custody hearing in August: “He’s the most beautiful person I’ve ever seen. He’s the love of our lives. He’s suffering a lot.”

Last week, the court recognized a California judgement that established Ahmed and Gilkar as the parents. The court dismissed West, who named the baby Gabriel, from the case.

In West’s appeal to the supreme court on Wednesday, her attorneys asked the justices to intervene on the Texas decision, arguing: “A stay is needed to preserve the status quo and ensure [West] can advocate for her rights and remain informed about [the baby] during this critical time in his young life.”

West’s attorneys said: “Irreparable harm from Texas’s enforcement of the California judgment matters immensely because [the baby] is in the midst of a course of several lifesaving surgeries needed to treat his condition.”

West also said in the filing: “The child could be removed from the Texas hospital and taken to California for hospice – despite his treatable condition – around September 17, if not sooner.”