Bachelet visited 14-year-old Valentina Maureira on Saturday after the girl's video went viral and spurred debate in Chile about euthanasia.
Valentina was diagnosed with cystic fibrosis when she was 6. Her older brother died from the same disease.
Cystic fibrosis is a life-threatening disease that damages the lungs and digestive system. Valentina's family has already witnessed how the disease can be terminal.
Valentina's suffering includes vomiting and headaches that are constant, according to her father, Freddy Maureira.
The teen recently posted a video on her Facebook page, asking Bachelet to allow her to end her life.
"I am tired of living with this sickness," Valentina says in the video. "Please authorize an injection so I can sleep forever."
Bachelet visited Valentina on Saturday for more than an hour at the hospital. The country's minister of health also attended.
During the visit, the President learned details about Valentina's health, whose condition has reportedly slightly improved, CNN Chile reported. The teen thanked Bachelet for the visit, and her father said he is holding on to hope for a lung transplant for his daughter, according to CNN Chile.
Before the visit, the President had already stated her position on the impossibility of an assisted suicide for the girl.
Not even the President can agree to Valentina's request because Chilean law does not allow euthanasia, Presidential spokesman Alvaro Elizaldo said.
"But what are we doing?" Elizaldo said last week. "The health ministry is in constant contact with Valentina's family, and we will provide all the emotional and psychological support and medical treatment to improve her living conditions."
Valentina's case has caused an overwhelming response on social media.
People took to Facebook and Twitter to discuss the debate on assisted suicide.
One Twitter user posed the question in a tweet: "After the case of Valentina Maureira, should euthanasia be legal?"
Doctor Andres Castillo, chief of pediatrics at Catholic University's Clinic Hospital, said that at the moment, Valentina's condition is stable."
After her diagnosis, doctors expected her to live to about 17, which would give her three and a half more years to live.