The Metropolitan Museum of Art’s decision to return 20 pieces from its collection to Italy could have a far-reaching impact for museums with artifacts of disputed origin.

The pieces the Met would give back include the Euphronios krater and a 15-piece set of Hellenistic silver, which are considered among the most valuable antiquities in the museum’s collection. The museum said it delivered a formal agreement proposal yesterday to officials at the Italian Ministry of Cultural Heritage in Rome.

Under the proposed agreement, the Met would transfer legal ownership of the disputed pieces to Italy in exchange for a series of long-term loans of works “of equivalent beauty and importance.”

The Italian cultural minister, Rocco Buttiglione, expressed satisfaction at the Met’s long-awaited decision, saying in a statement that it would “end all the controversy regarding the antiquities of Italian art illegally exported to the United States.”

The director of the Met, Philipe de Montebello, will travel to Rome later this month to finalize the deal, Mr. Buttiglione said.

Cultural scholars applauded the Met’s proposal, saying it could pressure museums across the country to return stolen art and may encourage other nations to pursue additional claims of looting, perhaps against the Metropolitan or other New York museums.

“I think it’s a good sign, and it’s certainly a long time coming,” the director of DePaul University’s program on cultural heritage law, Patricia Gerstenblith, said. “I think it will make it clear to these other museums that they have to consider similar kinds of cooperative and negotiated settlements.”

Ms. Gerstenblith said Italy was “generous” to the Met by offering the long-term loans instead of taking the museum to court.

The vice president of the Archaeological Institute of America, Brian Rose, said he was “delighted” by the proposed agreement. “I hope it’s only the beginning of a national trend,” Mr. Rose said.

The president and founder of the advocacy group Saving Antiquities for Everyone, Cindy Ho, said the deal could open the floodgates for claims of stolen artifacts at cultural institutions. “I actually do think this will be the beginning of countries asking for their objects to be returned,” Ms. Ho said. She cited Greece and Peru as countries that have recently been seeking the return of works they say were stolen. Whether the Met could face charges about pieces in its collection from other countries remains to be seen. “I think it’s possible,” Ms. Ho said.

A final agreement would resolve a dispute between Italy and the Met that has dragged on for decades. Italy has sought the return of several disputed pieces in the museum’s collection, especially the krater, a vase painted by the Greek painter Euphronios that dates to the fifth century B.C.E. The museum purchased the vase for a record $1 million in 1972.

In an effort to convince the museum of its claims, Italian cultural officials have cited evidence collected during investigations of an art dealer convicted of selling looted works, Giacomo Medici.

The museum has maintained that it would return the disputed pieces if presented with “convincing” evidence that they were stolen. Such evidence finally arrived last month, when Italy sent the museum a package of documents, including photographs, along with a formal draft agreement.

“We’re satisfied that the evidence suggests that this is the proper course,” a Met spokesman, Harold Holzer, said yesterday, referring to the museum’s offer.

If the Italians agree to the Met’s proposal, the museum could avoid a legal battle and any claims that it was liable for the alleged illegal export of the pieces from Italy. “In making this agreement, we are not acknowledging any kind of legal liability for those acquisitions or for holding the objects,” Mr. Holzer said. “We’re reiterating that they were acquired in good faith.”

Precisely when the museum’s pieces would physically return to Italy has yet to be determined. Italy could allow the Met to keep them on a long-term loan and then, after the loans expired, replace the pieces with loans of works from its own collections. Italian law now limits the term of a loan to four years, but it is possible the law could be changed or a loophole could be found.

Details of the loan arrangements and return of the pieces will be worked out in future talks, Mr. Holzer said.

Mr. de Montebello initially proposed the framework for a loan exchange agreement in a meeting with Mr. Buttiglione shortly before Thanksgiving in Rome. The Italian minister has since touted the idea, saying in a recent interview that he hoped it would be “the basis for similar agreements” with other museums the ministry planned to approach.

The negotiations with the Met have come as part of a broader push by Italian cultural officials to clamp down on illegal antiquities trafficking worldwide. The head of the J. Paul Getty Museum in Los Angeles, which has already returned several works to Italy, met with ministry officials last week in Rome to discuss other disputed antiquities in its collection. And an American art dealer, Robert Hecht Jr., and the Getty’s former antiquities curator, Marion True, are on trial in Italy on criminal charges that they conspired to sell looted art. Mr. Hecht is the dealer who sold the Euphronios krater to the Met, as well as the 15 pieces of silver, which the Italians say was looted from Morgantina, in Sicily. Mr. Hecht and Ms. True have maintained that they are innocent.

In agreeing to surrender the Euphronios krater, the Met is parting with a prized vase whose origin has been questioned since the day of its purchase, more than three decades ago. The museum’s director at the time, Thomas Hoving, bought the krater in 1972 from Mr. Hecht, who said he had acquired the piece from a Lebanese dealer claiming that his family had owned it since World War I. Both American and Italian officials were suspicious of the story, and in 1977, the Manhattan district attorney, Robert Morgenthau, launched an investigation and impaneled a grand jury. He halted the inquiry after a Chicago art dealer gave last-minute testimony that appeared to corroborate Mr. Hecht’s story.

In 2001, however, Italian investigators found a memoir by Mr. Hecht in which the dealer offers two different accounts of the krater’s origin. In one, he wrote that he purchased the Euphronios in 1971 from Medici, the Italian art dealer convicted in 2004 of selling looted art. The Italians also have photographs linking Mssrs. Medici and Hecht.

Still, the Met had until now been reluctant to relinquish what many say is its most prized antiquity.

“The acquisition was unwise from the beginning, and it took over 30 years for the Metropolitan to recognize both the legality and the ethics of the situation,” Ms. Gerstenblith said.

The mounting evidence long ago convinced Mr. Hoving, who has famously called the Euphronios a “hot pot.”

“I’m delighted,” Mr. Hoving said last night after learning of the Met’s proposal. “The hot pot is now no longer hot, and is legitimate. Finally, the Met and Italy have grown up.”

Mr. Hoving said he urged Italian officials to pursue the loan arrangement in a meeting last month. The Met stands to benefit from the deal as well, he said. “As collateral, it gets fantastic loans that nobody else can get.”