The Environmental Protection Agency, in a proposed rule, will aim to eliminate federal government requirements that the oil and gas industry put in place technology to inspect for and repair methane leaks from wells, pipelines and storage facilities.

The proposed rollback is particularly notable because major oil and gas companies have, in fact, opposed it, just as some other industries have opposed the Trump administration’s other major moves to dismantle climate change and other environmental rules put in place by President Barack Obama.

Some of the world’s largest auto companies have opposed Mr. Trump’s plans to let vehicles pollute more, while some electric utilities have opposed the relaxation of restrictions on toxic mercury pollution from coal-fired power plants.