Oil and gas companies, already reeling from sustained low prices, see an economic burden and have vowed to fight.

“It doesn’t make sense that the administration would add unreasonable and overly burdensome regulations when the industry is already leading the way in reducing emissions,” said Kyle Isakower, vice president for regulatory policy at the American Petroleum Institute. “Imposing a one-size-fits-all scheme on the industry could actually stifle innovation and discourage investments.”

The new methane rules are the latest part of a broader push by Mr. Obama to cut greenhouse gas emissions from industries across the economy. E.P.A. regulations would cut carbon dioxide emissions from cars, trucks and power plants, and new rules are in the works to reduce emissions from airplanes. Many of those regulations could face years of litigation before they can go into force.

The rules governing carbon dioxide emissions from cars and power plants, the two largest sources of greenhouse gas emissions, form the centerpiece of Mr. Obama’s climate change agenda. They are at the heart of his pledge under last year’s Paris Agreement on climate change that the United States would reduce its greenhouse gas emissions 26 percent to 28 percent from 2005 levels by 2025.

Reducing methane is an important part of the administration’s climate change strategy because the gas is 25 times more effective than carbon dioxide in trapping heat. It does, however, dissipate in the atmosphere far more quickly than carbon. The administration has set a goal of reducing methane emissions by as much as 45 percent from 2012 levels by 2025.