Heineman said he would call the Legislature into special session Nov. 14, the Omaha (Neb.) World-Herald reported. His announcement came as five children were left at hospitals in recent days.
The special legislative session must last at least seven days and will be limited to addressing the safe haven law, the newspaper said.
Speaker of the Legislature Mike Flood said he will introduce a bill that would restrict the law to babies in their first three days of life. Currently, the law allows parents to leave children of any age at hospitals.
"The circumstances dictate that we should act, and that's what will happen," Heineman said .
The latest cases in which the safe haven law was used both involved teens. On Tuesday, a 15-year-old Omaha girl was left by her father at Immanuel Medical Center in Omaha, and a 17-year-old boy was left by his mother and stepfather at BryanLGH Medical Center West in Lincoln.