A baby born with a rare heart defect who is at the center of a dispute between a surrogate and the parents underwent the first in a series of surgeries, a lawyer representing the child’s parents said Monday.

The baby, whom the parents have named Rumi, was born Wednesday in Texas with hypoplastic left heart syndrome, a rare heart defect that requires a series of surgeries, with the first typically happening during the first weeks of life. 

Lee Budner, the attorney for parents Omar Ahmed and Nausheen Gilkar, said the baby’s medical team determined Friday, “after thorough examination and imaging, that Rumi was eligible for a Norwood procedure, a complex palliative heart surgery that is the first of a series of three surgeries that are required within the first several years of life for babies born with HLHS.”

The procedure was performed Monday morning, Budner said, and “Rumi is now recuperating under the loving care of his parents and his heroic team of doctors, nurses, and medical staff.” 

“This is the last update on Rumi’s health that his family intends to share. His condition remains critical and complex, and his family seeks privacy in caring for their son on his long road to recovery,” Budner added.

The second surgery is usually performed at 4 to 6 months, and the third between 18 months and 5 years old, according to the Cleveland Clinic. The heart condition is rare and complex, the Cleveland Clinic says, and can cause lifelong complications. 

Several months before Rumi was born, when Gilkar and Ahmed learned of the heart defect, they asked the surrogate, McKenna West, to get an abortion, according to Texas Attorney General Ken Paxton, who intervened in the case last week. 

Gilkar and Ahmed are from California and West is from Alaska. West refused to get the abortion and instead went to Texas before the baby was born. 

Paxton had secured a court order saying the baby must receive lifesaving medical care after birth. The court also ruled that Gilkar and Ahmed are responsible for medical decisions within the requirements of the court order.

As a result of those orders, West was not allowed any contact with the child after his birth, her attorney, Lincoln Davis Wilson, told CBS News last week. Wilson said West intended to continue efforts to gain custody of the child, whom she had been calling Gabriel.

“We are working on challenging those orders of parentage because we think that Texas law makes a woman who gives birth [to] a child, the mother of the child,” he said last week.

CBS News has reached out to Wilson for comment.

Gilkar and Ahmed had previously asked a California court to order West to give birth there.

Budner said Monday that West “continues to assert baseless claims for custody of Rumi, in violation of multiple courts orders out of both Alaska and California. We look forward to quickly defeating those claims as Rumi’s parents continue to focus on his health and safety above all else.”