The group wants former Energy Secretary Rick Perry to argue for sanctions against the Saudis and Russia.
International producers are seeking cuts from US shale producers as well.
A Texas oil and gas regulator on April 2 said he talked with Russian Energy Minister Alexander Novak about the possibility of both Russian and Texan producers' trimming production.
Stabilizing the oil markets is expected to be a challenge because demand has collapsed.
The collapse in prices has threatened the once-booming U.S. oil and gas industry, which has a relatively high cost of production, leading Washington to scramble for ways to protect the sector.
When the three-year Saudi Arabia-Russia production-cut marriage known as OPEC+ ended acrimoniously on March 6, the oil and gas world as we know it ended. For now.
Crude oil prices ended a volatile quarter with their biggest losses in history, as both U.S. and Brent futures were hammered throughout March.
Texas Railroad Commission, the state's energy regulator, will weigh a mandated cut at its next scheduled meeting, said Ryan Sitton, the commissioner who first floated 10% cuts two weeks ago.
The collapse in demand and of energy diplomacy between Saudi Arabia, Russia and others have triggered unprecedented responses from governments and investors. Here are ten signs of an oil industry in distress.