Her assessment of the risk came before she was formally running for president. But two years later, in a television interview in October 2015, she sounded willing to take that risk. “I personally would be advocating now for a no-fly zone and humanitarian corridors to stop the carnage on the ground and from the air, to try to provide some way to take stock of what’s happening, to try to stem the flow of refugees,” she said.

Her successor as secretary of state, John Kerry, tried last month to open those humanitarian corridors, but the effort collapsed in a dispute with Russia. A push to get it restarted during a meeting in Lausanne, Switzerland, on Saturday between Mr. Kerry and his Russian counterpart, Sergey V. Lavrov, also failed.

In the talks at Goldman Sachs, Mrs. Clinton was often more analytic than prescriptive, describing her perceptions of individual leaders and the domestic politics and foreign threats they face. In that regard, her approach is quite different from that of Donald J. Trump.

In two interviews on foreign policy with The New York Times, one in March and another in July, Mr. Trump moved directly to his plans of action: bombing the Islamic State and taking oil, for example, or withdrawing troops from Europe and Asia if allies do not pay their share. While Mr. Trump often talks in terms of striking deals, Mrs. Clinton talks in the more traditional terms of alliance-building.

When she became secretary in 2009, she posed a question about China to an Australian leader: “How do you deal toughly with your banker?” In the Goldman transcript, she suggested that she had answered her own question when sparring with the Chinese over its claims in the South China Sea.

“I made the point at one point in the argument that, you know, you can call it whatever you want to call it,” she said. “You don’t have a claim to all of it. I said, by that argument, you know, the United States should claim all of the Pacific. We liberated it, we defended it. We have as much claim to all of the Pacific. And we could call it the American Sea, and it could go from the West Coast of California all the way to the Philippines.”

“And, you know, my counterpart sat up very straight and goes, ‘Well, you can’t do that.’”

Mrs. Clinton segued into an evaluation of Mr. Xi, the Chinese leader, who she noted had consolidated power in a way his predecessor never did, but had quickly traveled to places like Russia and Africa to assuage “doubts about Chinese practices.”