Culture Minister Francesco Rutelli of Italy said an offer by the J. Paul Getty Museum to hand over 26 disputed antiquities doesn’t go far enough and that the museum needs to return all of the artifacts that Italy has requested.

Italy is asking for 21 others, including “Statue of a Victorious Youth,” known as the Getty Bronze. The Los Angeles-based J. Paul Getty Museum, the world’s richest private art institution, said on November 21 that it would return only some of the contested objects.

“The next step is up to them,” Mr. Rutelli said at a Rome news conference. “There are lots of roads we can take,” including resuming talks, he added.

“The time for exhibiting obviously trafficked works of art is over,” Mr. Rutelli said.

In a statement issued after the press conference, the director of the Getty Museum, Michael Brand, said the museum was “deeply saddened” by Italy’s response, and he offered to continue talks. Mr. Brand invited Mr. Rutelli, who plans to be in America next week, to the Getty Villa, a museum of Roman, Etruscan, and Greek art, “so he can see for himself the impact the magnificent works of art displayed there have on the American public.”

The Getty joins other American museums that have been pressured to return artifacts and art to nations claiming ownership. New York’s Metropolitan Museum of Art said in February that it would return items that included a 2,500-year-old vase after Italy said the object had been looted.