The head of an Australian policy institute, Michael Fullilove, wanted to know if the United States, which shelved the Trans-Pacific Partnership Agreement and withdrew from the climate accord, was bringing about the destruction of the very global order Mr. Mattis was championing.

It was only the first question about the America’s new role in the world, which led Mr. Mattis to loyally defend Mr. Trump while trying to soothe anxieties. Trying to reassure his audience, Mr. Mattis argued that the American public had generally accepted that the country has global responsibilities despite occasional frustrations about the burden.

“To quote a British observer of us from some years ago, bear with us,” Mr. Mattis said. “Once we have exhausted all possible alternatives, the Americans will do the right thing,” he continued, invoking a famous quote often attributed to Winston Churchill.

“So we will still be there, and we will be there with you,” he added.

At another point, Mr. Mattis implored his audience to understand that just because the United States had backed away from the multilateral Pacific trade agreement “does not mean we are turning our back” on the prospect of negotiating bilateral trade agreements.

Mr. Mattis received some support Friday night from Australia’s prime minister, Malcolm Turnbull, who appeared to anticipate the mood of many participants at this annual conference organized by the International Institute for Strategic Studies, a research center based in London.