A bitter confrontation over surrogacy, abortion and parental rights that stretched across three states culminated on Wednesday with the birth of the baby at the center of the conflict at a Dallas hospital.

The fate of the baby, who has a severe birth defect, became a cause this summer among anti-abortion activists, who provided legal representation for the surrogate, McKenna West, and helped her travel to Texas for medical care. This week, she also received support from the Texas attorney general, Ken Paxton, who took legal action to compel medical treatments for the newborn.

The dispute began in the spring after the discovery at around 20 weeks of pregnancy that the fetus had a rare and life-threatening congenital heart condition, hypoplastic left heart syndrome, and would require multiple surgeries to survive.

The intended parents, who live in Los Angeles, opted to terminate the pregnancy.

But Ms. West, who lives in Alaska, refused to have an abortion. Instead, she went to Texas, which bans abortion, to seek specialists who could treat the baby’s defect.

On Wednesday, amid overlapping legal actions in the three states, Ms. West gave birth to a boy in Dallas whom activists have called “Baby Gabriel.” His legal parents, Omar Ahmed and Nausheen Gilkar, chose a different name.

“As if the heartbreak of his condition were not enough, they are devastated to see their family tragedy transformed into political theater by the Texas Attorney General’s office and McKenna West,” said a lawyer for the parents, Lee Budner, in a statement.

Mr. Budner said the boy was “now receiving medical care provided by a team of pediatric experts,” adding that the parents “would place their baby’s health and well-being first, following the advice of the baby’s medical team.”

Ms. West is seeking custody of the child.

The birth came just days after Mr. Paxton’s legal intervention on Monday. Mr. Paxton, a Republican locked in a tough race for the U.S. Senate, argued in Dallas County court that the parents were required to provide lifesaving care under Texas law.

“My office will use every tool available to protect innocent lives,” Mr. Paxton said in a statement.

The move sharply increased attention on what had already been a cause célèbre in anti-abortion circles this summer.

By Tuesday, Mr. Paxton celebrated having secured a temporary restraining order, or T.R.O., in Dallas that prevents the parents from removing the child from Texas until a hearing in late August. The order also requires them to provide “medically indicated, lifesaving treatment” to the baby.

At the same time, the Dallas County court also issued another restraining order against Ms. West. The order bars Ms. West from presenting herself as the baby’s parent, guardian or medical-decision maker “to anyone.”

“Unfortunately, because of the Texas T.R.O. that was entered yesterday, McKenna didn’t get to see or hold him after he was born,” Lincoln Wilson, a lawyer for Ms. West, said in an interview.

Ms. West, who did not respond to an interview request for this story, said in an interview this month with the former Fox News and current YouTube host Megyn Kelly that she did not support abortion and felt “trapped” by the surrogacy contract, which permitted the intended parents to end the pregnancy via abortion.

“It brought up a lot of fear,” said Ms. West, a nurse with two children of her own, in the interview.

Through a mutual friend, Ms. West connected with Lila Rose, the president of Live Action, an anti-abortion group. Ms. Rose said she helped Ms. West get legal support from the Alliance Defending Freedom, a prominent Christian conservative legal organization.

“There came a point where she, for the sake of her own medical care and safety, needed to travel to Texas, and so we did assist,” Ms. Rose said. “They were treating her baby like a product. The product had a defect, and so they were trying to send it back.”

Ms. Rose said that her organization does not support surrogacy, which “commoditizes human life” and leads to “heartbreaking and devastating situations like this.”

Mr. Wilson, the lawyer for Ms. West, said that the legal case was not over and that Ms. West would continue to fight for custody of the boy, who must undergo weeks of surgeries “before he’s really in the clear.”