WASHINGTON—The Trump administration is moving to erase Obama-era rules on methane emissions from the oil-and-gas business, saying the federal government overstepped its authority when it set limits on what scientists say is a significant contributor to climate change.

The sweeping proposal, formally introduced Wednesday, is the administration’s latest attempt to further boost record crude-oil and natural-gas production by easing regulations. But it comes amid growing concerns over how the industry’s methane emissions are affecting the climate and stark divisions among companies over whether to regulate them.

“The purpose of this rule is to get to the fundamental basis of whether [methane] should have been regulated in the first place,” said Anne Idsal, the acting assistant administrator for the Environmental Protection Agency’s Office of Air and Radiation, referring to the proposed rollback. “It’s not about whether we’re doing the maximum we can or should do to deal with” climate change.

“I don’t see that there’s going to be some big climate concern here,” Ms. Idsal added.

The vast majority of climate research identifies human-caused emissions as the primary driver of climate change, most commonly through carbon-dioxide emissions from sources including factories, planes and cars. But methane, which accounts for about 10% of U.S. greenhouse-gas emissions, is about 25 times more potent than carbon dioxide in trapping the earth’s heat, according to estimates used by the EPA. Its figures show the oil-and-gas industry has long been the nation’s largest emitter of methane, even before discoveries in shale and fracking led to a wave of new drilling.