WASHINGTON—The Environmental Protection Agency will propose a draft rule on Monday seeking a 30% reduction in carbon-dioxide emissions by 2030 from existing power plants based on emission levels from 2005, according to two people who have been briefed on the rule, setting in motion the main piece of President Barack Obama's climate-change agenda.

The rule, scheduled to be completed one year from now, will give flexibility to the states, which must implement the rules and submit compliance plans to EPA by June 2016. States...