WASHINGTON — President Obama will use his executive authority to cut carbon emissions from the nation’s coal-fired power plants by up to 20 percent, according to people familiar with his plans, which will spur the creation of a state cap-and-trade program forcing industry to pay for the carbon pollution it creates.

Mr. Obama will unveil his plans in a new regulation, written by the Environmental Protection Agency, at the White House on Monday. It would be the strongest action ever taken by an American president to tackle climate change and could become one of the defining elements of Mr. Obama’s legacy.

Cutting carbon emissions by 20 percent — a substantial amount — would be the most important step in the administration’s pledged goal to reduce pollution over the next six years and could eventually shut down hundreds of coal-fired power plants across the country. The regulation would have far more impact on the environment than the Keystone pipeline, which many administration officials consider a political sideshow, and is certain to be met with opposition from Republicans who say that Mr. Obama will be using his executive authority as a back door to force through an inflammatory cap-and-trade policy he could not get through Congress.

Image As governor of Massachusetts, Mitt Romney was a key architect of a cap-and-trade program in nine northeastern states. Credit... Jonathan Ernst/Reuters

People familiar with the rule say that it will set a national limit on carbon pollution from coal plants, but that it will allow each state to come up with its own plan to cut emissions based on a menu of options that include adding wind and solar power, energy-efficiency technology and creating or joining state cap-and-trade programs. Cap-and-trade programs are effectively carbon taxes that place a limit on carbon pollution and create markets for buying and selling government-issued pollution permits.