An Italian government official on Monday offered to end a long legal fight with the J. Paul Getty Museum by proposing shared custody of a 2,300-year-old bronze statue known as "Victorious Youth."

Italy claims the Getty procured the statue from illicit art dealers, which museum officials deny. Now, however, the governor of Italy's Marche Region—near where the statue was found—is trying both to resolve the matter and boost his home's profile among American tourists by proposing a "cultural exchange" between the Getty and his region.

"We have not come to declare war on the Getty," Gov. Gian Mario Spacca said at a hotel here Monday. "We are here to try to resolve the dispute in a way that will benefit this great museum, the people of Italy and, most important, art lovers around the world."

Getty officials said the object wasn't up for discussion because of the legal process. An Italian judge is expected to issue a decision in a few weeks.