California and New York issued a joint statement saying they would continue the fight against climate change.
Environmental groups have hired a host of lawyers to challenge Mr Trump's move that boosts fossil fuel production.
Mr Trump said he wanted to end "job-killing regulations".
His supporters believe that ending the climate change rules brought in by Barack Obama will create thousands of jobs in the gas, coal and oil industries.
The governors of New York and California summed up opponents' views by saying Mr Trump's stance was "profoundly misguided and shockingly ignores basic science".
In a joint statement, Governors Jerry Brown of California and Andrew Cuomo of New York, both Democrats, said: "With or without Washington, we will work with our partners throughout the world to aggressively fight climate change and protect our future."
The two states have set even stricter targets on reducing greenhouse gas emissions than required by Mr Obama's rules and have far-reaching plans for converting to renewable energy sources for producing electricity.
Governor Brown said: "Erasing climate change may take place in Donald Trump's mind, but nowhere else."
A host of legal issues could be in the pipeline.
California has a special waiver allowing it to enforce tougher measures on vehicle emissions. Mr Trump could rescind that - but this would lead to a fierce challenge.
He could also ask Congress to revoke the Clean Air Act.
Back in 2007, the US Supreme Court ruled that carbon dioxide gas was a pollutant under the Act.
Some experts believe that the ultimate goal of Mr Trump's executive order is to overturn that ruling.
Already tied up in the courts is Mr Obama's Clean Power Plan (CPP), which seeks to cut fossil fuels from electricity production.
David Goldston, of the Natural Resources Defence Council, said activists were gearing up for legal challenges.
He said: "The president doesn't get to simply rewrite safeguards; they have to... prove the changes are in line with the law and science. I think that's going to be a high hurdle for them."
Any legal challenges would dovetail with action to win over public opinion.
Jeremy Symons, of the Environmental Defence Fund, told Associated Press: "In terms of the big picture, our strategy is simple: shine a spotlight on what is going on and mobilise the public against these rollbacks."
But Mr Trump's move does have supporters.
US Chamber of Commerce president Thomas Donohue said: "These executive actions are a welcome departure from the previous administration's strategy of making energy more expensive through costly, job-killing regulations that choked our economy."
Mr Trump's Energy Independence Executive Order suspends more than half a dozen measures enacted by his predecessor.
Although during his election campaign he also vowed to pull the US out of the Paris climate deal agreed in December 2015, he has not spelled out the US intentions.
Whatever the US chooses, the EU, India and China say they will stick to their pledges made in Paris.
On Wednesday, Chinese foreign ministry spokesman Lu Kang said: "No matter how other countries' policies change, as a responsible large developing country, China's resolve, aims and policy moves in dealing with climate change will not."