“We’ve determined in the years after the theft that the art was transported to the Connecticut and Philadelphia regions,” Mr. DesLauriers said. “But we haven’t identified where the art is right now, and that’s why we are asking the public for help.” The splashy announcement, somewhat unusual when the identities of the suspects are known but not revealed, was designed to draw worldwide attention, he said, beyond the confines of Boston.

Bostonians have been obsessed with the case, and the museum reminds its visitors of the theft by keeping the empty frames that once held paintings like Rembrandt’s “The Storm on the Sea of Galilee” and Vermeer’s “The Concert” on display. That two large Rembrandt canvases were cut suggested that the thieves were novices in the value of the art. There have been no reports of the paintings having been fenced or sold.

Museum officials on Monday reiterated their promise of a $5 million reward for information leading to the recovery of the works in good condition. “You don’t have to hand us the paintings to be eligible for the reward,” said Anthony Amore, the museum security chief.

Ms. Ortiz said the statute of limitations had run out for the crime of art theft. Someone who had the paintings could still be charged with possession of stolen property, she said, but she also said there was a “very strong possibility” that such a person could receive immunity. Museum officials said their chief goal was to recover the art.

Special Agent Geoffrey Kelly of the F.B.I., who has been in charge of the Gardner investigation for about six years, said the works have most likely changed hands several times over the years. He also said it was possible that people possessing them might be unaware of their significance or that they were stolen.

“It is possible they have been asked at some point to take custody of something and don’t know what they have,” Mr. Kelly said.

Still, he said in an interview after the announcement, he was fully confident that the F.B.I. knew the identities of the men who broke into the museum. He gave no additional information and would not say whether they were dead or alive.