"Further surgery is not in the best interest of the Dogaru twins," the medical team at University Hospitals Case Medical Center Rainbow Babies Childrens Hospital in Cleveland, Ohio said in a statement.
"The decision not to move forward with the surgical separation was a difficult one, but it was made with the safety of the twins in mind. After countless hours of discussion and medical analysis, the Rainbow team feels that the risk of further surgery outweighs the likelihood of benefit."
The girls, Anastasia and Tatiana Dogaru, underwent a first round of separation surgery in June but the operation was halted due to brain swelling in the dominant twin, Anastasia.
The twins were born in Italy to parents of Romanian origin.
The top of Tatiana's head is fused to the back of her sister's head, in a rare medical disorder known as total angular craniopagus. The girls' brain tissue is connected and they share the same circulatory system.
Doctors have admitted the attempt to separate the girls, who also have heart, kidney and bladder defects, was "very high-risk."
The hospital has described their condition as comparable to being diagnosed with a malignant, inoperable brain tumor, noting that most cranial conjoined twins die at birth and only 10 percent live until the age of 10.
The hospital said physicians and nurses had "developed strong emotional ties to the girls and their family " and would do "all that we can to support the family as they make plans for the future."