Speaking in New Zealand following a trip to Antarctica, Kerry said his administration would continue to do everything possible to meet its responsibility to future generations.
Kerry has long championed climate action but now his legacy is under threat.
President-elect Donald Trump has called climate change a hoax and said he would "cancel" US involvement in the landmark Paris deal.
Under the deal, which came into force this month, countries have agreed to limit global warming to 2C above pre-industrial levels. Achieving the goal will require a major shift away from fossil fuels.
Kerry said it would be up to the Trump administration to define itself on climate change. He said that sometimes there is a divide between what is said on the campaign trail and what is done in governance.
But Kerry appeared to take a swipe at Trump when he listed some of the ways in which global warming could already be seen. He said that globally, there were more fires, floods and damaging storms, and sea levels were rising.
"The evidence is mounting in ways that people in public life should not dare to avoid accepting as a mandate for action," Kerry said.
He also made a point of crediting a previous Republican president, George H W Bush, with first joining the global effort to address climate change in Rio de Janeiro in 1992.
"Now the world's scientific community has concluded that climate change is happening beyond any doubt. And the evidence is there for everybody to see," Kerry said. "So we will wait to see how the next administration addresses this."
He said he thinks his administration is on the right track because the majority of Americans believe climate change is happening and want action.
Kerry plans to fly this week to a global climate conference in Morocco, where he will give a major speech. Officials there have begun working on a "rulebook" to implement the Paris deal.
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