The supreme court has refused to get involved with a custody dispute between an Alaska surrogate and a California couple whose child was born with a rare and serious heart defect.

On Tuesday, Justice Elena Kagan denied an emergency request from McKenna West, an Alaska nurse and surrogate who had asked the US’s highest court to halt a California court order recognizing the couple, Omar Ahmed and Nausheen Gilkar, as the boy’s legal parents.

In recent weeks, the case has garnered nationwide attention, sparking broader discussions about surrogacy and abortion.

In a 9 September filing, West’s attorneys urged the supreme court to intervene in what they described as “extraordinary circumstances”, arguing that “a life hangs in the balance”.

Following a scan that discovered the baby having hypoplastic left heart syndrome, a condition that impedes blood flow and requires extensive surgery, Ahmed and Gilkar asked West to abort the pregnancy. According to NBC, the couple signed a contract last August with West that included a clause stating that the pregnancy could be terminated in the case of a “fetal abnormality”.

However, West refused to terminate the pregnancy and instead traveled to Texas, where abortion is illegal, to give birth. Republican attorney general Ken Paxton intervened, shining a national spotlight on the case. A Dallas judge subsequently issued an order requiring the baby to receive medical care.

Kagan’s refusal to intervene comes just days after the Texas supreme court ruled that the month-old child can leave Texas and relocate to a Los Angeles hospital for treatment.

“Sustaining the life of the medically fragile child is the paramount concern in this time-sensitive matter,” the court said.

West has since argued for custody of the child, claiming that his legal parents will not provide the necessary medical care because they had previously sought an abortion.

West’s attorneys say that because their client “is now completely excluded from the life of the medically fragile infant she brought into the world, much less from the ability to make critical health decisions that protect him, time is of the essence”.

In West’s filing to the supreme court, her lawyers argued that “without relief, she will receive no further information about the child she carried for 37 weeks and fought to save”.

During a court hearing in Dallas last month, the child’s parents said West was “unstable”. Gilkar added: “He’s our child … He’s the most beautiful person I’ve never seen … He’s the love of our lives. He’s suffering a lot.”