Emma and Taylor Bailey of the Queen Creek area died Tuesday at Seattle Children's Hospital during an operation on their shared heart.
CBS station KPHO in Phoenix said doctors were trying to increase the pressure of the heart they shared. The two were born connected at the chest and shared a liver and a seven-chambered heart. Most hearts have four chambers.
Family friend Ginni Christiansen said Thursday that the girls had had the surgery twice before but this time an artery burst and doctors were unable to save them.
The girls had defied medical expectations and would have turned 4 next month. They had been scheduled to undergo a risky operation to separate them later this year.
Fundraisers have been held to help the family and last year dozens of celebrities joined in with a dinner theater production in the Phoenix area.