At his death, Mr. Amano was engaged in a diplomatic challenge with little or no precedent: He was trying to convince Iran to stay within the strictures of the nuclear deal even though Mr. Trump had abandoned it last year. His effort worked until recent weeks, when Iran began inching away from compliance in order to force Europe to compensate it for American-imposed sanctions on its oil revenues.

Finding a replacement for Mr. Amano will not be easy; large and small powers always struggle over who should run the agency. Mr. Amano was sometimes accused by the Iranians and others of being too solidly in Washington’s camp. But in Washington, the Trump administration and critics of the Iran deal — including the Israelis — argued that Mr. Amano was not aggressive enough in demanding access to suspected nuclear sites and that he too easily accepted Iranian declarations about the history of its nuclear program.

At his death, however, even some of the I.A.E.A.’s critics inside the Trump administration praised Mr. Amano’s efforts to navigate some of the world’s most perilous nuclear politics. John Bolton, for one, President Trump’s national security adviser, said in a statement that Mr. Amano’s death was a “great loss for Japan, the United States, and to many, many people from around the world.”

Even the Iranians said they mourned the man with whom they had argued with over what the agency could inspect and what they thought was off-limits. Seyed Abbas Araghchi, Iran’s deputy foreign minister and a negotiator on the nuclear deal, said on Twitter on Monday that he had worked closely with Mr. Amano.

“I commend his skillful & professional performance,” as the head of the agency, Mr. Araghchi wrote.

Fluent in English and French, Mr. Amano often showed that he was in full command of both the technical details of producing nuclear fuel and the politics of keeping that fuel from being turned into nuclear weapons.