China, the EU and India, which along with the US make up the four biggest emitters of carbon dioxide, have restated their commitment to the 2015 Paris Agreement on climate change.
Top EU official Donald Tusk said at a summit with China that Brussels and Beijing would step up co-operation.
Mr Trump announced the US was leaving for economic reasons, saying the deal would cost American jobs.
Secretary of State Rex Tillerson said the US would still curb emissions.
Amid widespread international condemnation of the US decision, Russian President Vladimir Putin said he would "not judge" Mr Trump.
The Paris agreement commits the US and 194 other countries to keeping rising global temperatures "well below" 2C above pre-industrial levels and "endeavour to limit" them even more, to 1.5C.
The UN World Meteorological Organisation said on Friday that, in the worst scenario, the US pullout could add 0.3C to global temperatures by the end of the century.
What do the EU and China say?
European Council President Donald Tusk said after meeting Chinese Premier Li Keqiang that the two powers took their responsibilities seriously.
"Today, China and Europe have demonstrated solidarity with future generations and responsibility for the whole planet," he told reporters at a joint news conference.
"The fight against climate change and all the research, innovation and technological progress it will bring will continue with or without the United States," he added.
Mr Tusk was echoing similar pledges by EU politicians such as German Chancellor Angela Merkel who said the path set out by Paris was "irreversible".
A spokeswoman for the Chinese foreign ministry, Hua Chunying, said China was ready to take a leading role in the fight against climate change.
"In the future, China will continue to tackle climate change in all ways, will proactively participate in the multilateral process of tackling climate change and resolutely uphold the global climate management process," she said.
Indian Environment Minister Harsh Vardhan said: "As far as the Paris accord is concerned... our government is committed, irrespective of the stand of anyone, anywhere in the world."
The group of the world's 48 least developed countries accused Mr Trump of showing disregard for millions of lives.
Scientists have warned the poorest countries across the globe will be the hardest hit by climate change as they lack capacity to cope with extreme weather events.
Why is Trump pulling out?
Mr Trump characterised the Paris agreement as a deal that aimed to hobble, disadvantage and impoverish the US.
He said it would cost the US $3tn (£2.3tn) in lost GDP and 6.5 million jobs - while rival economies like China and India were treated more favourably.
Mr Trump said he was fulfilling his "solemn duty to protect America and its citizens".
Secretary of State Rex Tillerson said the US had a "terrific record on reducing our own greenhouse gas emissions".
The head of the US Environmental Protection Agency, Scott Pruitt, said exiting the Paris Agreement did not mean disengagement.
"The president said yesterday that Paris represents a bad deal for this country," he told reporters at the White House.
"It doesn't mean that we're not going to continue the discussion to export our innovation, to export our technology to the rest of the world, to demonstrate how we do it better here."
The Russian president said he thought the US did not need not to abandon the Paris Agreement because it was a "framework".
Can it all be renegotiated?
Under the terms of the agreement, the US cannot complete its withdrawal until just weeks after the US presidential election in 2020.
US payments to the UN Green Climate Fund, which helps developing countries cope with the effects of climate change, will stop. The US has reportedly so far paid $1bn (£780m) of a $3bn pledge.
Mr Trump indicated he was open to another climate deal "on terms that are fair to the United States" but the leaders of France, Germany and Italy quickly issued a joint statement rejecting any renegotiation.
What are they saying in America?
The Democratic governors of New York, California and Washington states all quickly vowed to respect the terms of the Paris deal.
Disney's chief executive Robert Iger and the entrepreneur Elon Musk both resigned from White House advisory councils in opposition to the decision.
However, Republican congressional leaders and the US coal industry backed the move, with Senate Majority Leader Mitch McConnell supporting Mr Trump "for dealing yet another significant blow to the Obama administration's assault on domestic energy production and jobs".
Peabody Energy, America's biggest coal mining firm, said the agreement would have badly affected the US economy.
What was agreed in Paris?
Climate change, or global warming, refers to the damaging effect of gases, or emissions, released from industry, transportation, agriculture and other areas into the atmosphere.
The Paris accord is meant to limit the global rise in temperature attributed to emissions. Only Syria and Nicaragua did not sign up.
Countries agreed to:
- Keep global temperatures "well below" the level of 2C (3.6F) above pre-industrial times and "endeavour to limit" them even more, to 1.5C
- Limit the amount of greenhouse gases emitted by human activity to the same levels that trees, soil and oceans can absorb naturally, beginning at some point between 2050 and 2100
- Review each country's contribution to cutting emissions every five years so they scale up to the challenge
- Enable rich countries to help poorer nations by providing "climate finance" to adapt to climate change and switch to renewable energy
Nasa's Goddard Institute for Space Studies says the world's average temperature has risen by about 0.8C since 1880, two-thirds of that since 1975.
US think tank Climate Interactive predicts that if all nations fully achieve their Paris pledges, the average global surface temperature rise by 2100 will be 3.3C, or 3.6C without the US.