"Continuing to question the science and hurl insults at 'global warming hoaxsters' and 'apostles of this pseudo-religion' won't prevent severe damage to our health and economic well-being," Brown wrote in a letter. "Americans, their children and generations to come deserve – and demand – better."
Brown, a Democrat, said California's drought and wildfires are evidence that the effects of climate change are being felt now, calling it "the new normal."
The governor added, "Lest you think this movement is limited to Democrats and only embraced within our borders, the conservatives in England, the moderates in Germany and even the communists in China are on board."
Many of the Republican candidates, who are participating in their first debate on Thursday, have either denied the science surrounding climate change or opposed stiffer steps to address the problem.
It's a key issue for Brown, who has pushed stronger regulations in California and taken shots at Republicans on the issue before.
In March, he said Ted Cruz, the U.S. senator from Texas, had shown "such a level of ignorance" that he "has rendered himself absolutely unfit to be running for office." More recently he labeled politicians who deny the existence of climate change as "troglodytes."
Brown, 77, ran for president three times himself, in 1976, 1980 and 1992. Asked earlier this year if he would run again if he was a decade younger, he said, "Yes, I would."
Then, the governor added, "If I could go back in a time machine and be 66, I might jump in. But that's a counterfactual, so you don't need to speculate on that."