WASHINGTON — Aiming to jolt the rest of the world to action, President Obama moved ahead Sunday with even tougher greenhouse gas cuts on American power plants, setting up a certain confrontation in the courts with energy producers and Republican-led states.

In finalizing the unprecedented pollution controls, Obama was installing the core of his ambitious and controversial plan to drastically reduce overall U.S. emissions, as he works to secure a legacy on fighting global warming. Yet it will be up to Obama’s successor to implement his plan, which has faced steep Republican opposition from Capitol Hill to the 2016 campaign trail.

Opponents planned to sue immediately, and to ask the courts to block the rule temporarily. Many states have threatened not to comply.

The White House estimated the emissions limits will cost $8.4 billion annually by 2030. Energy industry advocates said the revision makes Obama’s mandate even more costly and difficult to achieve.

Last year, the Obama administration proposed the first greenhouse gas limits on existing power plants in U.S. history, triggering a yearlong review. On Monday, Obama was to unveil the final rule publicly at the White House.

“Climate change is not a problem for another generation,” Obama said in a video posted to Facebook. “Not anymore.”

The final version imposes stricter carbon dioxide limits on states than was previously expected: a 32 percent cut by 2030, compared to 2005 levels. Obama’s proposed version last year called only for a 30 percent cut.

Immediately, Obama’s plan began reverberating in the 2016 presidential race, with Hillary Rodham Clinton voicing her strong support.

“It’s a good plan, and as president, I’d defend it,” Clinton said.

But Republican presidential candidate Marco Rubio, a Florida senator, predicted electricity bills would go up for millions of Americans and called Obama’s policies on power plants “catastrophic.”

Obama’s rule assigns customized targets to each state, then leaves it up to the state to determine how to meet them. If states refuse to submit plans, the EPA has the authority to impose its own plan.