The surprising move is a blow to the administration and a victory for the coalition of 27 mostly Republican-led states and industry opponents that call the regulations "an unprecedented power grab."
By temporarily freezing the rule the high court's order signals that opponents have made a strong argument against the plan, which aims to stave off the worst predicted impacts of climate change by reducing carbon dioxide emissions at existing power plants by about one-third by 2030. A federal appeals court last month refused to put it on hold.
The appeals court is not likely to issue a ruling on the plan until months after it hears oral arguments begin on June 2. But any decision likely would be appealed to the Supreme Court, meaning resolution of the legal fight is not likely to happen until Obama leaves office.
The high court's four liberal justices said Tuesday they would have denied the request for delay.
Compliance with the new rules isn't required until 2022, but states must submit their plans to the Environmental Protection Administration by September or seek an extension.
Many states opposing the plan depend on economic activity tied to such fossil fuels as coal, oil and gas. They argued that power plants will have to spend billions of dollars to begin complying with a rule that may end up being overturned.
Attorney General Patrick Morrisey of West Virginia, whose coal-dependent state is helping lead the legal fight, hailed the court's decision.
"We are thrilled that the Supreme Court realized the rule's immediate impact and froze its implementation, protecting workers and saving countless dollars as our fight against its legality continues," Morrisey said.
Implementation of the rules is considered essential to the United States meeting emissions-reduction targets in a global climate agreement signed in Paris last month. The Obama administration and environmental groups also say the plan will spur new clean-energy jobs.
To convince the high court to temporarily halt the plan, opponents had to convince the justices that there was a "fair prospect" the court would strike down the rule. The court also had to consider whether denying a stay would cause irreparable harm to the states and utility companies affected.