These latest talks are aimed at developing the rules for implementing the accord signed in the French capital in 2015.
But there is a growing worry that President Trump might soon pull out of the historic deal.
Some delegates say such a move would be a body blow for the landmark deal.
The May meeting of the UN climate talks body is normally a pretty low-key affair but this is the first gathering of delegates since Donald Trump was inaugurated. Many are worried that it could also be the time the new president decides to pull the plug on US participation in the Paris deal.
"This was supposed to be a highly technical and uneventful meeting to flesh out some of the details in the Paris Agreement. But, obviously, the speculation coming out of Washington is now at the top of our minds," said Thoriq Ibrahim, minister of environment and energy for the Maldives and chair of the Alliance of Small Island States.
"We continue to believe that the agreement is not only central to averting the worst impacts of the climate crisis, including the loss of entire nations to sea-level rise, but also our ability to address problems that can only be solved by the international community working together."
During the presidential campaign, Mr Trump railed against the Paris climate agreement. He said he was going to "cancel" a deal that has now been ratified by more than 140 countries and legally entered into force last November.
In office, President Trump has been concerned with removing environmental regulations that he believes are an unnecessary hindrance to the coal, oil and gas industries.
The president also asked the US Environmental Protection Agency to re-write the Clean Power Plan, the key Obama-era scheme to cut US carbon emissions by 32% by 2030. It was the key commitment made by the US during the Paris climate negotiations. The new president wants to significantly weaken that plan.
Many commentators believed that on the Paris agreement, Mr Trump was starting to listen to voices, including Secretary of State Rex Tillerson, who argue for staying in the deal, saying it is important for the US to "maintain its seat at the table".
That view has also been supported by some of America's biggest corporations.
"We are for staying in the treaty. I think global engagement is a good thing," GE chairman Jeff Immelt told students at Georgetown University last week. "As a company, we think that climate change is real."
However, recent speculation suggests that members of the Trump administration who want to pull out of Paris are gaining the upper-hand.
This group of advisors, said to include chief strategist Steve Bannon and White House chief of staff Reince Priebus, argue that if the president tries to lower US targets for cutting emissions while still in the deal, he could be sued by green groups.
"Those urging the president to withdraw from the agreement have manufactured a misleading debate over whether the terms agreed to in Paris could be used to challenge the administration's plans on climate change," said Paula Caballero from the World Resources Institute, and a former climate negotiator for Columbia.
"Walking away from the agreement would be a dark stain on President Trump's legacy that he would never be able to wash out."
Behind the scenes there are ongoing efforts by negotiators to convince the US that leaving would be bad not just for the Paris agreement but also for America.
Some are floating the idea that the US should be allowed to change or even reduce its commitments to cut carbon as long as it stays in the deal.
"We all continue to hope the US will find a way to remain within the Paris Agreement and to remain committed to the Paris goals," said EU climate commissioner Miguel Arias Cañete.
"The Paris Agreement allows each country to forge its own path to contributing to the goals of preventing dangerous climate change. 195 countries have signed the Paris Agreement and there will be 195 different paths to meeting the Paris goals. So there is room for a new US Administration to chart its own path as well."