The forthcoming proposals from the E.P.A. and Interior Department would allow far more methane to leak from oil and gas drilling operations, environmentalists say. “These leaks can pop up any time, anywhere, up and down the oil and gas supply chain,” said Matt Watson, a specialist in methane pollution with the Environmental Defense Fund, an advocacy group. “The longer you go in between inspections, the longer leaks will go undetected and unrepaired.”

The proposals exemplify President Trump’s policy quest to roll back regulations on businesses, particularly oil, gas and coal companies. While significant aspects of the president’s broader agenda — including immigration and trade policy, and the proposed border wall with Mexico — remain mired in confusion, and as the administration struggles under the investigation into the presidential campaign’s ties with Russia, the E.P.A. and Interior Department have steadily pressed forward with rollbacks of environmental regulations.

“In other areas of policymaking, like immigration and health care, they appear to have brought into the administration ideologues who don’t know a lot about policymaking,” said Cecilia Muñoz, who directed the White House Domestic Policy Council in the Obama administration. “But in climate change and energy, they appear to have brought in people who know exactly what they’re doing, and know exactly where the levers are.”

The pace of the proposals has not been slowed by the resignation in July of Scott Pruitt, who left the top job at the E.P.A. under a cloud of ethics scandals. Andrew Wheeler, a former coal lobbyist who worked in the E.P.A. under the first President George Bush, is now the agency’s acting chief.

The E.P.A.’s new methane proposal, according to the draft seen by The Times, would loosen a 2016 rule that required oil and gas drillers to perform leak inspections as frequently as every six months on their drilling equipment, and to repair leaks within 30 days. The proposed amendment would lengthen that to once a year in most cases, and to as infrequently as once every two years for low-producing wells. It would also double the amount of time a company could wait before repairing a methane leak from 30 to 60 days.

It would also double the amount of time required between inspections of the equipment that traps and compresses the natural gas, from once every three months to once every six months. On the Alaskan North Slope, where oil and gas companies contend that harsh weather makes it difficult to conduct inspections, such equipment would only have to be monitored annually.

In addition, the E.P.A. proposal would let energy companies operating in states that have their own state-level methane standards follow those standards instead of the federal ones. That would include states such as Texas, where the pollution standards have been more lax than federal standards.

If implemented, the proposal would recoup nearly all the costs to the oil and gas industry that would have been imposed by the Obama-era regulation. The E.P.A. estimated that rule would have cost companies about $530 million by 2025. The E.P.A. estimates that the proposed changes would save the oil and gas industry $484 million by the same year.

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