Authorities are searching for the girl in Arizona, California and Mexico, where the family has relatives, as doctors say she could contract a potentially deadly infection if not returned for treatment.
The girl underwent about a month of chemotherapy and had been treated for an infection that forced doctors to amputate her arm, police said. Doctors had inserted a tube through her chest to deliver medications through her heart. Her mother unhooked the tubing from an IV and left with the girl, leaving her susceptible to infection.
Phoenix police said the parents could face criminal neglect charges if they didn't return the girl.
U.S. Border Patrol agents stopped the father, Luis Bracamontes, 46, as he crossed into Arizona from Mexico over the weekend, but the man denied any involvement in removing his daughter from the hospital and said he didn't know where she was.
However, in an interview this week with NBC News, Bracamontes said his daughter was safe and being treated by doctors in Mexico.
"She is well and she is fine," he said while declining to reveal where the girl was being treated.
Bracamontes blames the Phoenix hospital for the loss of his daughter's arm and says the family was being pressured over mounting medical bills. He displayed photos of the girl both before and after the surgery and talked on his mobile phone to a girl and a woman he claimed were his daughter and wife.
The hospital cannot comment on Emily's condition due to health privacy laws, but in a statement Wednesday said decisions about patient care are not based on ability to pay.
"Phoenix Children's Hospital is deeply concerned about Emily's safety and well-being and continues to cooperate with law enforcement," the hospital statement read. "If Emily's family has questions about her care, we encourage open communication and discussion of options with the care team. "
Phoenix police, meanwhile, say the father's story raises even more red flags.
"We're in the same spot we were in last Thursday when we began looking for her," police Sgt. Steve Martos said Wednesday. "We understand the right of a parent to change doctors, to change hospitals, we're not challenging that. We just want to make sure that Emily is getting the right medical attention that she requires to prevent this potential horrific ending."
Martos said doctors in Phoenix told authorities that if Emily's catheter is not tended to, it could make her susceptible to a deadly infection that could kill her in a matter of days.
Dr. William Schaffner, an infectious disease specialist at Vanderbilt University Medical Center, said Emily's immune system is already compromised from the cancer and chemotherapy.
"If bacteria get into the blood stream, that can cause a serious infection," Schaffner said.
The open catheter could serve as a pathway for bacteria, he said, adding that a potentially deadly infection is not only possible, but likely.
Martos said the father's story only adds to investigators' bewilderment that began when the mother inexplicably removed the child from the hospital. He said surveillance video shows the mother and child getting into a dark-colored minivan, but the license plates on the car were registered to a different vehicle.
"It all just makes us even more curious that they're unwilling to provide us with basic information to confirm what he is saying, and they're still trying to hide Emily," Martos said. "There's certainly the potential for some criminal charges."
"So we're going to continue looking for her until we either run out of leads or she is found," he added. "We can't just drop it."