BADEN-BADEN, Germany — The United States broke with other large industrial nations over trade on Saturday as the Trump administration rejected concerns among allies about spreading protectionism and made clear that it would seek new approaches to managing global commerce.

At a meeting of finance ministers and central bankers from the Group of 20 industrialized and emerging nations and the European Union, Steven Mnuchin, attending his first major international gathering as Treasury secretary, signaled that American policy would follow the campaign promises made by President Trump to put “America first” and review existing trade agreements to seek better deals for the United States.

As a result, the ministers’ joint statement, normally a study in blandness, became an unlikely focus of controversy here. The representatives could agree only on a tortured compromise stating, in effect, that trade is a good thing. Adjectives like “open” were dropped, and the ministers omitted language used in previous communiqués that condemned protectionism, repudiating decades of free trade doctrine.

For Asian and European officials, many of them meeting their Trump administration counterparts for the first time, it was a startling lesson in how Mr. Trump and his team are overturning long-held assumptions about international commerce.