In April, the states, D.C. and the environmental organizations separately notified the EPA that they were prepared to sue the agency within 60 days over delay of the rules.
The EPA proposed carbon emissions standards for new power plants last April, but has not yet finalized the rules. Climate advocates also want EPA to require standards for currently operating plants.
In their letter, the 21 attorneys general refute the other states' claims and assert that the EPA is only required by the Clean Air Act to update its standards "if appropriate."
"We therefore request that EPA refrain from allowing petitioners to unduly influence the policymaking process via settlement negotiations," they write.
This week, the states and environmental groups announced that they were delaying their lawsuits in response to indications that the White House will unveil a major climate change plan in July.
Attorneys general from Virginia, Ohio, Florida and Kentucky were among those that signed the letter to the EPA on Tuesday.
This post was updated at 6:53 p.m.