A bipartisan group of U.S. senators rolled out a bill Thursday that would allow the Justice Department to sue members of OPEC for antitrust violations as the oil cartel looks to formalize closer ties with Russia.

Sens. Chuck Grassley (R., Iowa), Amy Klobuchar (D., Minn.), Patrick Leahy (D., Vt.) and Mike Lee (R., Utah)—all members of the Senate Judiciary Committee, where the bill would likely be considered before being taken up by the full Senate—unveiled the legislation. That comes one day after The Wall Street Journal reported that Saudi Arabia and its Persian Gulf allies are backing a formal partnership with a 10-nation group led by Russia to try to manage the global oil market. Such an alliance would transform the cartel.

“The oil cartel and its member countries need to know that we are committed to stopping their anticompetitive behavior,” Mr. Grassley said in a statement.

The senators dubbed their bill the No Oil Producing and Exporting Cartels Act, or NOPEC. Separately, the House Judiciary Committee on Thursday unanimously advanced a parallel measure that will now require approval by the full House.

The proposal by the Organization of the Petroleum Exporting Countries would formalize the loose union between OPEC members and the group led by Moscow, which includes some former Soviet republics and other countries including Mexico.

OPEC’s proposal runs counter to President Trump’s goal of lowering gasoline prices for U.S. consumers ahead of presidential elections next year. But it could ultimately benefit a booming U.S. oil industry and increase the nation’s energy independence.

A representative for Senate Judiciary Chairman Lindsey Graham (R., S.C.) couldn’t immediately be reached for comment. A spokesman for Senate Majority Leader Mitch McConnell (R., Ky.) declined to comment, but Senate Republican leadership typically allows votes on bills that President Trump supports or measures that otherwise don’t divide the GOP caucus.

Secretary of State Mike Pompeo on Wednesday criticized OPEC’s plans to formalize closer ties with Russia.

“Vladimir Putin would love that, and it’s not going to happen under President Trump,” Mr. Pompeo said in a Wednesday interview on the Fox Business Network. “I am very confident that Vladimir Putin’s efforts will fail.”

Saudi Arabia has been pushing for a firmer alliance that would lead to higher oil prices because the nation is in need of more cash.

The 14 OPEC members and the 10 allies led by Russia have increasingly worked together in recent years, including in December when they agreed on a deal to curb production to address an oversupplied global crude market. They groups had first collaborated in 2016 to help oil prices rebound following a two-year crash.

But Russia is willing to go only so far in part because of moves like the NOPEC legislation. Moscow rejected a proposed formal partnership in December, specifically citing antitrust concerns.