European leaders have promised to pressure Trump, an avowed sceptic, on the need to maintain a united front in the fight against global warming.
Terrorism and trade may top the agendas, especially in the wake of Monday's Manchester massacre that left at least 22 dead.
But European leaders have promised to pressure Trump, an avowed sceptic, on the need to maintain a united front in the fight against global warming.
"I am still trying to convince the doubters," German Chancellor Angela Merkel said Tuesday at informal 30-nation climate talks in Berlin, where China's climate tzar, Xie Zhenhua, also urged the United States to stay the course.
Newly minted French President Emmanuel Macron, on the eve of his May 7 victory, likewise vowed to "do everything possible" to keep the former reality TV star on board. Macron intended to press the climate case at a one-on-one "working luncheon" in Brussels on Thursday, an Elysee advisor told AFP.
Even Pope Francis made a point on Wednesday of giving Trump a copy of Laudato Si, the Pontiff's impassioned plea for preventing the planet from overheating.
Trump has said he will pass judgement on the landmark 2015 climate treaty -- which he trashed as a candidate -- upon returning to Washington. There are hints he may show his hand during Friday's G7 summit in Sicily, the last stop on his 10-day foreign foray.
Simply ignoring the topic at the rich-nation summit is not really an option, said David Waskow, a veteran climate analyst at the World Resources Institute, a Washington-based think tank.
"Climate change has been mentioned in every G7 and G8 outcome over the past 30 years, and over the past decade it has been a central part of every communique," Waskow told journalists in a briefing.
If climate change goes unmentioned, in other words, it would be an unmistakable sign of disaccord.
Any end-of-summit joint statement will probably seek to remain strategically vague, analysts said.
In their role as hosts, "the challenge for the Italians is to let the American president go away saying 'we didn't go any further,' and for the rest of the countries to be able to say 'we didn't go backwards'," said Tom Burke, Chairman of E3G, a London-based climate policy think tank.
If the US president is to be swayed, it may be pressure from business interests that makes the difference.
A host of metrics -- the stabilisation of CO2 emissions from energy production, investment in renewables outstripping fossil fuels -- point to a decisive shift in the global economy towards clean energy, and for many businesses the risk of getting left behind now outweighs the cost of joining in that transition.
Even big oil and coal have backed the Paris Agreement, which leaves room for technologies that would allow these industries to grow in a low-carbon economy.
A major report from the Organisation for Economic Co-operation and Development (OECD) released this week underscores that change.
"Far from being a dampener on growth, integrating climate action into growth policies can have a positive economic impact," said OECD Secretary-General Angel Gurria.
The report calculates that merging growth and climate agendas could add one percent to average economic output in G20 countries -- which account for 85 percent of global GDP, and 80 percent of CO2 emissions -- by 2021.
By mid-century, output could go up by 2.8 percent, the report finds. And if the benefits of avoiding impacts such as coastal flooding and sea level rise are factored in, the net increase in GDP would be nearly double that figure.
"The real world has already made up its mind," said Burke. "The flows of capital have made it clear that we are looking at a landscape of economic opportunity, not economic constraint."
Climate change has also emerged as a "threat multiplier" for illegal migration and terrorism, both key issues on the table as Trump met with NATO leaders in Brussels on Thursday.
New research, for example, is detailing how conflict and water shortages in the Middle East and north Africa -- with five percent of the world's population but less than one percent of its renewable water supply -- could trigger a mass exodus from affected areas.
No matter what Trump decides to do, the potential for disruption remains.
"Even if the US stays in the Paris Agreement, no one really knows what the administration's stance will be," said Alden Meyer, director of strategy and policy for the Union of Concerned Scientists in Washington.
Trump has vowed to cut off international climate funding, and has already undercut domestic efforts to reduce greenhouse gas emissions -- the two main pillars of the Paris pact.