And Renatt Brodsky, a spokeswoman for Mount Sinai, said on Saturday that the hospital system would follow the executive order “effective today.”

“We have always — and will always — make these difficult decisions with the best of intentions and safety of the mother, baby and our staff as our guiding principle,” Ms. Brodsky said.

Mount Sinai updated its policy on its website Saturday night, saying all visitors would still be barred from the postpartum recovery area.

Dr. Christopher Zahn, the vice president of practice activities for the American College of Obstetricians and Gynecologists, emphasized the value of support persons in labor and delivery rooms in a statement on Friday.

“Evidence suggests that, in addition to regular nursing care, continuous one-to-one emotional support provided by a partner or support personnel such as a doula is associated with improved outcomes for women in labor,” Dr. Zahn said.

He added, “Labor support can be particularly critical for women who already face health care disparities and other barriers to care.”

Jesse Pournaras, a New York City-based doula who brought the petition opposing the new policies, said the decision was a victory on behalf of women giving birth in New York City and beyond.