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Aucklander Troy George Skinner pleaded guilty to one charge of producing child pornography.
The 28-year-old was arrested in June 2018 after he showed up at the home of the girl, whom he had met online and allegedly tried to break in.
Authorities say the girl's mother shot him, and Skinner has since recovered from a bullet wound to his neck.
The special agent in charge of the Federal Bureau of Investigation's Richmond field office, Stanley M. Meador, said that the FBI would investigate any matter where people prey on children.
"Mr. Skinner's solicitation of this minor victim is unfortunately not uncommon for sexual predators; what is rather unusual is for a predator to travel this extensively to gain access to their victim.
"Had it not been for the intervention of an adult, this incident could have been much worse."
Sentencing for Skinner is set for February next year.