Justice Elena Kagan on Tuesday refused to intervene in a custody battle over a baby born via surrogacy, leaving a lower-court order giving custody to the biological parents in place.

The case drew national attention when surrogate Mc Kenna West, from Alaska, refused an abortion after the fetus was diagnosed with hypoplastic left heart syndrome. She traveled to Texas and gave birth on Aug. 12. The baby boy received open-heart surgery and remains in a Dallas hospital.

The couple, Nausheen Gilkar and Omar Ahmed of California, asked Ms. West to terminate the pregnancy, citing their contract. A California court recognized them as parents in June. Texas Attorney General Ken Paxton intervened to ensure medical care but later dropped out.

Ms. West's lawyers said she was denied control over the child's care. The couple's lawyers said they are providing lifesaving care and that "a right to life is not at issue here."