But it is far from certain that Mr. Ban can get enough countries to add up to the 55 percent threshold. No other countries have close to as many carbon emissions as China or the United States. The world’s third-largest carbon polluter, India, which emits about 7 percent of the world’s emissions, has been unclear about its plans to sign on. Although India’s prime minister, Narendra Modi, emerged as a key broker of the Paris agreement, many members of his government remain wary of taking the final steps to clinch the deal.

Rajendra M. Abhyankar, a former Indian minister of foreign affairs who is now a professor at Indiana University, said, “While many in our government want to go forward with the terms of the agreement, there is still a feeling that ratifying the agreement would be tying our hands in terms of what we can do economically.”

“And from an international point of view, the sense is, why should we sign on if the United States might one day drop out?” he said. “The United States has signed on for now, but what will happen once Trump comes?”

Another question mark is the European Union, whose 28 member countries together account for about 10 percent of global emissions. Under the Paris agreement, the union has pledged to collectively reduce its emissions 40 percent below 1990 levels by 2030. But the union cannot legally ratify that pledge until all 28 countries have separately ratified it in their own parliaments, a process that could take years. The British vote to leave the European Union could further complicate that process.

Within the union, advocates of the Paris deal who fear a Trump presidency have pushed for new legislation that would allow the body to quickly ratify the Paris deal with executive authority — or would allow individual countries to ratify it separately from the union. But those proposals are already creating political rifts within the European body.

In the face of such difficulties, Mr. Ban has redoubled his diplomatic efforts. In recent weeks, he has met with or telephoned dozens of world leaders, including Mr. Modi, to urge them to complete their ratification of the Paris deal by Sept. 21. At the Chinese summit meeting of the Group of 20 largest industrial economies this month, he pressed the issue with every world leader present, according to aides.

He is seeing some success. On Monday, Brazil, which emits about 2 percent of global emissions, announced that it had completed its domestic ratification of the Paris deal. That came as a surprise to many, since Brazil’s climate pledge had been a signature policy of Dilma Rousseff, the country’s recently impeached president.