A conservative group is sending a stop work order to all states in the wake of Tuesday's decision by the Supreme Court halting President Obama's climate rules for power plants.

"States cannot be punished for waiting, since under the stay the compliance timeline no longer applies," the American Energy Alliance said Thursday. "With the stay in place and the future of the rule in jeopardy, there is no reason for states to move forward until litigation concludes."

That's why in response to the high court's 5-4 decision to stay the rule, called the Clean Power Plan, the group is mailing "stop work" orders to all state governors, public utility officials and other regulators charged with adopting a plan to comply with the Environmental Protection Agency's plan that directs states to cut their emissions a third by 2030.

The group points out that "given the court's unprecedented decision, any action to comply before legal resolution would be imprudent and a disservice to ratepayers." The statement echoes those made Wednesday by state attorneys general leading a coalition of 29 states against the plan in the D.C. Circuit Court of Appeals, which will hear their arguments on the merits of their case in June.

In the meantime, the high court approved their request that a stay be implemented to avoid harm to states from higher energy costs and changes to the energy mix. The states argue that the rule is illegal under the Clean Air Act.

The stop work order says continuing work would result in lost jobs, higher electricity rates, compliance with an illegal regulation and electric grid instability. "As a country, we should focus on ways to make electricity more affordable, not on implementing regulations that will raise energy costs, which hit the poor and middle class the hardest," the group's president, Tom Pyle, said in a statement to the Washington Examiner.

The group notes that even EPA Administrator Gina McCarthy says implementation is stalled until court action has been resolved.

"Nothing is going to be implemented while the stay is in place. It is clearly on hold until it resolves itself through the courts," she told the House Agriculture Committee.

Later, McCarthy spoke at a two-day Clean Power Plan compliance workshop attended by governor-appointed energy officials and state commissioners, where she encouraged states that want to keep working on compliance to do so. She said that a group of states has already made aware that they are planning to do so, and that the agency's air office chief and senior counsel will be using their frequent flyer miles to connect with states who still want to talk.

She said to the "pundits" that the EPA "remains fully confident in the legal merits of this rule," and the high court's stay "doesn't mean they spoke to the merits."

"Let's keep celebrating, let's keep moving forward," she said.