By Natalie Andrews and Andrew Scurria

Five New York-based members of Congress are asking their state's attorney general to probe whether investment firms that own billions of dollars in Puerto Rico bonds concealed aspects of their investments to manipulate prices and profit unfairly.

In a letter sent Wednesday, the Democratic lawmakers, led by Reps. Alexandria Ocasio-Cortez and Nydia Velázquez, asked New York Attorney General Letitia James to investigate allegations of insider trading utilizing the Martin Act, a broad antifraud statute commonly used to pursue financial crime, or other similar laws.

"Although hedge funds have secured generous settlements and made billions off this crisis, it now appears that their greed may have driven some New York financial institutions to take illegal actions," said Ms. Ocasio-Cortez, a critic of the management of Puerto Rico's debt crisis.

Ms. James' office didn't immediately respond to a request for comment on the letter.

The letter concerns allegations that a bondholder committee took public positions that drove down the price of certain debt securities while its members bought them at discounted prices and negotiated a restructuring proposal that improved how they would be repaid.

The lawmakers said those bond trades may have been made without proper disclosure of the "true economic interests" of bondholders, including Aristeia Capital LLC and Taconic Capital Advisors LP.

Puerto Rico's financial oversight board, which is steering the bankruptcy and leading negotiations, declined to comment.

A spokesman for the bondholder committee said its members "adhered to and respected all elements of the mediation protocol and trading restrictions during the period in which they were negotiating."

"As creditors with long-term investments in Puerto Rico, our members have consistently engaged in a constructive, transparent manner with the oversight board to facilitate the Commonwealth's timely emergence from bankruptcy and economic recovery," the spokesman said.

The New York attorney general recently attempted to use the Martin Act in a case against Exxon Mobil Corp., alleging that the oil giant misled investors about how it accounts for the impact of climate change on its operations by using internal estimates that differed from its public statements.

New York State Supreme Court Justice Barry Ostrager ruled in December last year that the attorney general's office didn't prove that the company had violated the law. Lawyers for Exxon said the company had done nothing wrong.

Wednesday's letter said the Martin Act could be used to investigate possible wrongdoing by Puerto Rico bondholders "and ensure the integrity of the municipal bond markets."

Write to Natalie Andrews at Natalie.Andrews@wsj.com and Andrew Scurria at Andrew.Scurria@wsj.com