David Renz admitted in county court that he carjacked the two on March 14, stabbing and strangling the mother to death as she tried to stop him from raping her daughter.
Renz had been under federal monitoring after a child pornography charge and a federal judge was sharply critical of the way probation officers failed to keep track of him.
Renz, 29, pleaded guilty to state charges of first-degree murder and sexual assault against a child. He was expected to be sentenced to life in prison without the possibility of parole, but the plea bargain can be withdrawn if the federal government seeks the death penalty.
Reading stiffly from a statement as his lawyer looked over his shoulder, Renz described the crimes and said he did not "fully understand" what led him to attack the mother and child.
"But even if I did, an explanation is not a justification nor does it lessen my responsibility for what I've done," he said, at times stumbling over the words.
"I'm truly sorry for my actions and I am prepared to accept the consequences for them," he said. "I hope that by pleading guilty, I will be able to bring closure for the victim and her family."
Authorities say Renz attacked the woman, a school librarian, and her daughter after they left a gymnastics class at a mall in the Syracuse suburb of Clay.
Prosecutors say Renz was trying to use cable ties to bind the woman to a headrest in her car when she fought back and shouted for the girl to bolt from the vehicle. As the girl ran off and was rescued by a passing motorist, her mother was strangled and repeatedly stabbed in the head and chest, officials said. Renz was captured by police shortly after.
The Associated Press generally does not identify victims of sex crimes and has not identified the woman to protect the identity of girl.
Hours before the attack, Renz removed and quickly reassembled an electronic bracelet so monitors didn't immediately realize he'd taken it off, authorities said. He was ordered to wear the device as a condition for being released from jail after his arrest in January on federal child pornography charges.
Weeks after the attack, a report by a federal judge found that the officers failed to do monthly checks on Renz that would have included inspection of the bracelet. Federal probation officers Syracuse who were monitoring Renz were fired or demoted.
Sentencing was set for Nov. 1.