Clinton is scheduled to meet the prime minister, Fredrik Reinfeldt, on Sunday. They are expected to discuss the EU financial crisis, internet freedom and several key foreign policy questions including Syria.
She arrived in the Swedish capital after a short trip to neighbouring Norway.
After a visit on board a research ship outside the Norwegian town Tromsö, Clinton said she was not surprised but still worried when she was shown several signs of climate change, the news agency TT reports.
"Even if it might seem an overwhelming task to mitigate the effects of global warming we can all do something," she said.
She said the USA will seek to co-operate with Norway when it came to the Arctic, where receding ice is unveiling significant oil and gas reserves, and called the two nations "Arctic allies".