The EPA briefly considered tucking a delay of Obama-era landfill methane rules into its major power plant plan.

The change, ultimately rejected, would have pushed back by more than two years the deadline for states to submit plans to comply with the Environmental Protection Agency’s limits on methane, a potent greenhouse gas, from existing landfills.

The waste industry is seeking revisions to the Obama-era limits, and companies are hoping any changes will be final by May 2019, when they would...