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."

Puerto Rico entered bankruptcy in 2017 under the weight of crushing government debts, spiraling pension obligations and a poverty rate over 40%. While the bankruptcy has crushed the value of many of the U.S. territory's bond debts, some savvy investors have profited handsomely, buying bonds on the cheap that have rallied on expectations about how much they will recover.

Since the bankruptcy, some investors have argued that older government bonds should be treated more favorably in a restructuring, saying that more recent debt issuances breached debt limits in Puerto Rico's constitution and should be reduced or disallowed.

Bondholders generally have to disclose the size of their investments in court filings, but weren't always required to break down which securities they owned. That changed in May, when the federal judge overseeing the bankruptcy case ordered the submission of more detailed disclosures.

Some bondholders later revealed they owned bonds they had said publicly "were of no value" while "engaging in confidential mediation talks about their restructuring," according to the New York lawmakers. A restructuring proposal released after those restructuring talks included higher recoveries for some of the older, disputed bonds compared to earlier discussions, rallying prices.

The lawmakers' letter called for an investigation "to reveal whether some hedge funds may have made these trades with non-public information obtained through the mediation discussions."

Other large creditors in Puerto Rico's bankruptcy have hinted at similar concerns about bondholder disclosures. In March, financial guarantors with billions of dollars on the line asked for greater transparency and raised concerns about bond trading based on "non-public information." They later amended their court filings to remove those allegations.

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