The comments were the strongest yet from the alliance about the importance of upholding the deal, which was signed by 195 countries in the French capital last year.
They come amid lingering tensions between Mr Trump and the leaders of Nato, an organisation the President once called "obsolete".
"There is a huge necessity that the UN continues to involve all nations and co-ordinate the action of all nations to fight climate change," said General Denis Mercier, Nato's supreme allied commander for transformation.
"If one nation, especially the biggest nation... if they do not recognise a problem, then we will have trouble dealing with the causes of climate change."
Though he did not single out any country by name, the United States is the world's largest economy and the second biggest emitter of greenhouse gases after China.
The Paris deal pledged to limit global warming by reducing greenhouse gas emissions, and to provide funds to poorer countries dealing with the effects of climate change.
Mr Trump has repeatedly complained the US was treated unfairly in the agreement, which requires it to pay more tax than other countries to fight global warming.
His predecessor, former President Barack Obama, pledged the US would drastically cut its greenhouse gas emissions by 26-28 per cent from 2005 levels by 2026.
Nato has a duty to try and predict the impact of greenhouse gases on geopolitical stability, Mr Mercier, who is French, explained.
He said risks include rising sea levels, water shortages and the opening of access to resources in the Arctic - all of which he said are likely to bring about new conflicts that could involve the 28 Nato countries.
But he said a global effort to stem climate change could help the world avert some of these potential crises.
"It's not too late, but it is time," he added.
US greenhouse gas emissions have fallen recently due to a switch from coal to natural gas and renewables in generating electricity. But many climate experts fear that if Washington leaves the Paris accord, or reduces its commitments, other countries could follow suit and global emissions could surge.
Many companies, including ExxonMobil Corp, Microsoft Corp, and Arch Coal Inc, have urged the US to stay in the Paris agreement, in part to retain their global competitiveness.
Mr Trump, who has said in the past the concept of global warming was "created by the Chinese in order to make US manufacturing non-competitive", is expected to announce his decision in the next fortnight.