“It is clear that the consensus that the world had up until the G-20 in Germany is no longer the same,” Nicolas Dujovne, Argentina’s treasury minister said, referring to last year’s summit meeting.

Bill Morneau, Canada’s finance minister who has been engaged in tense negotiations with the United States to overhaul the North American Free Trade Agreement, said the Trump administration was showing little sign of being more accommodating to the trade worries that have gripped of the rest of the world.

“I have the continuing sense that they have a point of view, and that point of view is that the system has to work in a way that, in their estimation, benefits American businesses and American trade,” Mr. Morneau said. “The ramifications of that are that we’re going to have to rethink some of the rules.”

Trump administration officials have said that the tariffs are aimed primarily at combating cheap metals from China, which they say are flooding into the United States through other countries. The Commerce Department has ruled that those imports pose a threat to national security because they degrade the United States’ industrial base.

Countries including France, Argentina and South Korea pressed Mr. Mnuchin during the gathering about being freed from the metals tariffs, arguing that, as United States allies, they should not be penalized on national security grounds. Mr. Mnuchin said that decisions were being made on a case-by-case basis and that there was not a one-size-fits-all approach to deciding which countries would be exempt. The tariffs go into effect on Friday.

Mr. Trump has already said he would exempt Canada and Mexico from the tariffs upon a successful renegotiation of Nafta, and he has indicated that other countries could also get exemptions. But the United States has yet to detail what would qualify a country for an exemption, other than a vague reference to protecting the United States’ national security and reducing bilateral trade deficits.

In an interview on the sidelines of the meeting, Mr. Mnuchin suggested exemptions to the tariffs could be announced “relatively quickly.”