At one point, another father, Edgar Ramirez, 25, said, security guards kept him out of the neonatal unit for three hours while his wife and newborn were waiting for him. At another point on Saturday, a guard declared that “the floor is on lockdown,” Ms. Nash-Coulon said, and told her that if she left the neonatal unit, she would not be allowed back in to see her babies.

“It was just really disgusting,” said Ms. Nash-Coulon, 38, who is still recovering from her C-section, while one of her twins remains in the hospital. “We really believe the hospital is culpable in this because they didn’t let us know what was happening. And the security of our children is at risk when you cover security cameras.”

Ann Silverman, a spokeswoman for Lenox Hill, part of North Shore-Long Island Jewish Health System, said the hospital had received no formal complaint about security measures, while taking care not to confirm or deny the birth of Blue Ivy, who was celebrated in a rap song released on Jay-Z’s social Web site on Monday as “the most beautiful girl in the world.”

“We have been in control of the security detail, and we remain in control of it,” Ms. Silverman said. “The security plan was designed not to limit access to patient care areas.”