Trump's decision two weeks ago to pull out of the landmark pact was "a sign of abdication from common action", Juncker told the European Parliament.
Trump has made a vague suggestion that he could try to renegotiate terms with better guarantees for US industry.
"The European Union will not renegotiate the Paris Agreement," Juncker told the assembly in Strasbourg, France.
"Climate action does not need more distractions. We have spent 20 years negotiating. Now it is the time for action," he said.
Polluting the Paris agreement
Juncker said he saw "strengthened resolve" around the world to implement the deal, vowing to work with other US partners like the states of California and New York as well as China and Canada.
The Paris pact was signed by the United States and 194 other nations in 2015.
Juncker said EU climate commissioner Miguel Arias Canete would host talks with his Chinese and Canadian counterparts in September to forge ahead with implementing the pact.
Marshall Islands President Hilda Heine, speaking in Strasbourg, called for EU help in fighting climate change as her Pacific archipelago is exposed to climate-induced sea level rises.
Juncker promised not to let her down.
Trump and the Paris agreement
"Madame President, we will work to help your country continue to mark the beginning of our days. We will not allow the denial of the very few to be the end of the days of the Marshall Islands," he said.
The day after Trump announced Washington was pulling out of the Paris agreement, Juncker and European Council President Donald Tusk met with Chinese Premier Li Keqiang to support the Paris agreement.
But the two sides failed to endorse a joint statement because of a separate trade row that EU officials said did not undermine their determination to fight climate change.
The United States is the world's second-largest greenhouse gas emitter, after China, so Trump's decision could seriously hamper efforts to cut emissions and limit global temperature increases.
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