Washington (CNN) California and New York filed a lawsuit Friday to try to block the Trump administration from revoking the states' authority to set their own vehicle emission standards.

Earlier this week, President Donald Trump announced he was revoking the authority for California, saying in a tweet that it would "produce far less expensive cars for the consumer, while at the same time making the cars substantially SAFER."

The state's waiver under the Clean Air Act allowed it to set standards tighter than the federal standards, which have been adopted by more than a dozen states and became the de-facto nationwide standard, because automakers do not design different sets of vehicles to meet different standards in different states.

The lawsuit, which was filed in federal court in Washington, DC, was signed onto by attorneys general from more than two dozen states and cities -- including the District of Columbia -- led by Democrats. Among other things, the states argue that the move by the administration would infringe on their authority and interfere with their ability to "to address greenhouse gas emissions and other air pollution."

The plaintiffs also claim that the move would cause an increase in greenhouse gas emissions, thus interfering with their ability "to meet their greenhouse gas reduction targets or mandates."

Read More