OMAHA, Neb. &#8212 A former New York elementary school principal admitted in federal court Monday that he had flown four times to Nebraska to have sex with a 15-year-old girl he had met on the Internet.

John Monetti, 38, pleaded guilty to two counts of travel with intent to engage in a sexual act with a juvenile.

In a plea bargain, other federal charges were dismissed: sexual exploitation of a juvenile and computer enticement of a minor.

U.S. District Judge Joseph Bataillon told Monetti that he likely will spend 12 years in a federal prison, then asked Monetti whether he agreed with the sentence.

“Yes, I do,” Monetti replied.

Bataillon set a sentencing hearing for Nov. 9.

Monetti, of St. James, was principal of William Floyd Elementary School on Long Island. He was arrested at his parents’ home in St. James.

Starting in December 2005, prosecutors said, Monetti began an Internet conversation with the girl, then 14, who lived near Blair.

Monetti later bought her a cellular phone so her parents would not become suspicious of their conversations.

In April 2006, Monetti made the first of four weekend flights from Long Island to Omaha to spend time with the girl, who had turned 15.

He rented a motel room in Blair, which is about 20 miles north of Omaha. He had sexual intercourse with the girl in the motel room and inside a rental van. He bought her several gifts.

Monetti was arrested in Washington County on May 29 last year, when deputies found him in a rental van with the girl. Monetti was driving; the girl was in the front passenger seat, wearing pajamas.

Monetti was charged in state court and released on bail in June 2006; the state charges of first-degree sexual assault of a minor, sexual assault with use of a computer, and child abuse.

Shurie Graeve, the Washington County attorney, said Monday that state charges were dropped in April to get out of the way of the federal case.

“I don’t anticipate refiling,” she said, “but I’ll wait to see what happens on sentencing” of Monetti in federal court.

When he was arrested, Monetti was working as a substitute teacher in the Commack School District on Long Island.

He previously served as principal at the Dickinson Avenue Elementary School in the Northport-East Northport School District, and at William Floyd Elementary.