Baby Gabriel's Biological Parents Authorize Heart Surgery After Initially Wanting Abortion

2:30 PM PT -- Lee Budner, attorney for the child's biological parents, tells TMZ ... the baby underwent surgery this morning and "is now recuperating under the loving care of his parents and his heroic team of doctors, nurses, and medical staff."

Budner tells us ... "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."

He adds ... "Meanwhile, Ms. 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."

We're told the Norwood procedure is the first of three surgeries required within the first several years of life for children born with hypoplastic left heart syndrome.

The biological parents who wanted their surrogate to terminate the pregnancy are now taking steps to keep their newborn alive ... telling a judge they've decided their son will undergo major heart surgery.

According to a court filing, obtained by TMZ, Nausheen Gilkar and Omar Ahmed have elected to have the baby undergo the Norwood procedure after consulting with doctors at Children's Health.

The Norwood procedure is a complex open-heart surgery performed on newborns with hypoplastic left heart syndrome -- the condition doctors discovered during the pregnancy. It helps the side of the heart that works pump blood through the body.

The parents call their son Rumi in the filing. Surrogate McKenna West referred to him as Gabriel ... though Nausheen and Omar say that is not his name.

The filing does not reveal when the operation will take place, but the parents say they will provide the date privately if the court requests it.

As we reported ... after doctors discovered the heart defect at the 20-week scan, Nausheen and Omar invoked a clause in the surrogacy agreement requiring West to terminate the pregnancy.

West initially scheduled the procedure ... then changed her mind and traveled from Alaska, where she lives, to Texas, where she gave birth early last week.