Liao Guojun, the father, told CNN Wednesday the girls suffer from more than 10 illnesses and their chance of survival is "very low."
The children were born May 5 in China's southwest Sichuan province, in the small city of Suining.
"The doctor said they are in critical condition," Liao said. "The girls suffer from more than 10 illnesses right now and their chance for survival is very low."
Liao said the infants, called the 'left sister' and the 'right sister,' bring he and his wife much joy, even if their condition is critical.
"They cry at the same time, they sleep at the same time and they wake up together and sometimes their hands wiggle in the air, grabbing for each others hand," Liao said. "It's very cute."
Doctors say the twins wouldn't survive a surgery to separate them because they share one heart and part of another. The twins also share a spleen, gallbladder and have one reproductive system.
The infants were transferred from Suining to Xin Qiao Hospital in Chongqing, where they can be better cared for, CNN said.
The hospital classified the babies as "high risk" and said they suffer from a variety of illnesses, including anemia, pneumonia, jaundice and neonatal sepsis.
Apple iPhone 6 goes on sale globally
U.S. monitoring terror plots from al-Qaida