Federal authorities are struggling to crack down on what they describe as a widespread scheme that has already likely defrauded the Internal Revenue Service of billions of dollars using the stolen identities of Puerto Rican citizens.

The perpetrators of the scheme, authorities say, swipe the Social Security numbers of Puerto Rican citizens, who don't have to pay federal income tax—and are less likely to be on the IRS radar—and use their information to file fake returns. In some cases, they enlist U.S. mail carriers to intercept the refund checks that are disbursed.

The plot, which includes participants from around the U.S. and Latin America, has been around for at least five years. Prosecutors have obtained multiple convictions but none involving those believed to be among the top players in the operation, according to several people briefed on investigations into the fraud.

"What we have uncovered may very well be the tip of the iceberg," said Manhattan U.S. Attorney Preet Bharara, whose office was among the first to investigate the group. "It's a massive fraud."

Between October 2010 and June 2011, the IRS received phony tax returns based on stolen Puerto Rican identities that would have led to the disbursement of $5.6 billion to alleged fraudsters, two of these people said. It is unclear how much money the IRS ultimately sent but one person familiar with the matter said an estimated $2 billion in checks was distributed.