FRANKFURT — South Korea made an impassioned appeal to the American secretary of defense and national security adviser, reminding them of its role trying to defang North Korea. Europe pointed out that it was, in fact, a longstanding military ally of the United States.

But it was Australia that deployed a secret weapon a day after President Trump signed an order imposing tariffs on steel and aluminum imports, as nations jockeyed for exemptions from the levies.

“We’re calling in all contacts at every level,” Julie Bishop, Australia’s foreign minister, told the Australian Broadcasting Corporation. Top among those enlisted: the golfing legend Greg Norman, a friend of Mr. Trump’s. “We will continue to push our case, we’ll continue to advocate on behalf of Australia for as long as it takes,” she said.

In seeking to win a respite from the tariffs, American allies tried a mix of persuasion and threats, personal appeals and diplomatic leverage. But they faced a delicate balancing act. A country that offers something in return for an exemption could set a precedent, allowing the White House to make further demands in the future in return for access to the United States market, and fracture any sense of unity between capitals from Brussels to Seoul that have roundly criticized the tariffs.