Italy’s supreme court has ruled that the Getty museum in Los Angeles must return a 2,000-year-old bronze statue it bought for almost $4m (£3.1m) in 1977.

The museum has vowed to defend its “legal right” to the ancient Greek statue of Victorious Youth, also known as Athlete from Fano or simply the Getty Bronze, which was made by Greek sculptor Lysippos between 300 and 100 BC, after the court said it must be returned to Italy.

The bronze statue was discovered by fishermen off Pesaro, on Italy’s Adriatic coast, in 1964, sold several times, and eventually bought by the American museum over 40 years ago.

But Italy has always maintained that it was smuggled out of the country and acquired illegally, making its first formal request for its return from the US in 1989.

After an 11-year legal battle, the supreme court rejected an appeal by the J Paul Getty Museum against an order from the Pesaro judge Giacomo Gasparini in June for the statue to be confiscated.

Pesaro prosecutor Silvia Cecchi told Italian media that the supreme court ruling was “the final word from the Italian justice [system]” and that the Lysippos statue “must be returned”.

The statue of a Victorious Youth is among the most popular works at the Los Angeles museum.

Culture minister Alberto Bonisoli urged US authorities to act quickly on the country’s behalf to “favour the restitution of the Lysippos to Italy”.

“I am happy that this judicial process has finally ended and the right to recover an extremely important piece of our country’s heritage has been recognised,” he added.

Italy’s battle over the statue included a letter to the US president, Donald Trump, from art critic Vittorio Sgarbi calling on him to ensure its restitution.

But the museum has refused to surrender the relic, saying it would appeal against the decision. The museum argued that the statue was discovered in international waters and pointed out that it was acquired by the museum nine years after Italy’s top court concluded there was no evidence that the statue belonged to Italy.

“The court has not offered any written explanation of the grounds for its decision, which is inconsistent with its holding 50 years ago that there was no evidence of Italian ownership,” Lisa Lapin, Getty’s vice-president of communications, said in a statement.

“Moreover, the statue is not and has never been part of Italy’s cultural heritage. Accidental discovery by Italian citizens does not make the statue an Italian object. Found outside the territory of any modern state, and immersed in the sea for two millennia, the Bronze has only a fleeting and incidental connection with Italy.”

Experts dispute this. The fishermen who found the artefact sold it in Fano, a town in Pesaro province, to Italian art dealer Giacomo Barbetti. Barbetti kept the statue in his father’s home before it was transferred to the Umbrian town of Gubbio in 1965, where it was eventually sold to an unidentified buyer from Milan. The statue then changed hands several times before being bought by the Getty.

“Italy has made a very clear and compelling case that the Lysippos was smuggled into Italy, via Fano, and therefore was later smuggled out of Italy,” Noah Charney, an arts professor who teaches each summer on the Arca postgraduate program in art crime and cultural heritage protection in Italy, told the Guardian.

“Where it was first discovered, whether in Italian or international waters, is therefore a moot point.”

Tristano Tonnini, a lawyer for Le Cento Città, an association leading the fight for the statue’s return, said he was convinced that the Getty museum of “always knew it was buying a smuggled and illegally exported artefact”.

The statue is among the most popular works at the Los Angeles museum, but its legal ownership has been in dispute ever since Getty bought it from German art dealer Herman Heinz Herzer in 1977.

The sum paid was nearly 800 times the $5,600 that Italian art dealers gave to the fishermen who found it.