Environmental advocates described the proposal as a major setback in the effort to fight climate change. Methane is a potent greenhouse gas.

“The Trump E.P.A. is eager to give the oil and gas industry a free pass to keep leaking enormous amounts of climate pollution into the air,” said David Doniger, a lawyer with the Natural Resources Defense Council, an advocacy group. “If E.P.A. moves forward with this reckless and sinister proposal, we will see them in court.”

Under the proposal, methane, the main component of natural gas, would be only indirectly regulated. A separate but related category of gases, known as volatile organic compounds, would remain regulated under the new rule, and those curbs would have the side benefit of averting some methane emissions.

The new rule must go through a period of public comment and review, and would most likely be finalized early next year, analysts said.

Over all, carbon dioxide is the most significant greenhouse gas, but methane is a close second. It lingers in the atmosphere for a shorter period of time but packs a bigger punch while it lasts. By some estimates, methane has 80 times the heat-trapping power of carbon dioxide in the first 20 years in the atmosphere.

Methane currently makes up nearly 10 percent of greenhouse gas emissions in the United States. A significant portion of that comes from the oil and gas industry. Other sources include cattle and agriculture.

The E.P.A.’s economic analysis of the rule estimated that it would save the oil and natural gas industry $17 million to $19 million a year. For comparison, the annual revenue of the United States oil industry as a whole typically ranges between $100 billion and $150 billion.