WASHINGTON — President Obama’s new plan to fight climate change depends heavily on states’ devising individual approaches to meeting goals set in the nation’s capital, a strategy similar to the one he used to expand health care, often with rocky results.

Rather than imposing a uniform standard for reducing power plant carbon emissions, the regulation unveiled on Monday offers the states flexibility to pick from a menu of policy options. But as with health care, the policy could lead to a patchwork of rules that frustrate businesses and invite resistance from states that oppose the policy.

Monday’s announcement of the proposed regulation — which is intended to cut carbon pollution from power plants by 30 percent from 2005 levels by 2030 — represented Mr. Obama’s boldest step in using his executive authority to halt the warming of the planet, an issue he vowed to address during his first presidential campaign six years ago.

Largely welcomed by environmentalists, the plan generated a torrent of criticism from industry, coal-state lawmakers from both parties and Republican leaders who called it a job-killer that would raise utility costs.