USA treasury secretary Steven Mnuchin, taking part in his first worldwide meeting since being sworn in, sought to downplay the wording.
"We want to reexamine certain agreements, we have talked about reexamining NAFTA", he told journalists, referring to the North American Free Trade Agreement between Canada, Mexico and the United States.
Rather than omit trade from the statement altogether, he said he wanted to find a formulation all could agree.
At this weekend's gathering of the Group of 20, the world's 20 largest economies, the group took a step back from its typically overt pro-free trade agenda, in the wake of pushback from the United States.
Mnuchin said that language was "in the past" and "not really relevant".
Asked about climate change funding, Mick Mulvaney, Trump's budget director, said on Thursday: "We consider that to be a waste of money".
Schaeuble said the adopted list of principles included policy recommendations for example on labor market regulation, but also for worldwide trade and the "importance of open markets".
The world's top economic powers have dropped a pledge to fully oppose trade protectionism amid pushback from the US government of President Donald Trump, who wants to favor American companies and workers more.
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China and European countries had pushed for a stronger affirmation of cross-border trade without tariffs or barriers.
The communique, which was published at the end of the meeting in Baden-Baden with the agreement of all attending delegates, also failed to include a vow on climate change. He has already pulled the USA out of the proposed Trans-Pacific Partnership agreement with Japan and other Pacific Rim countries and he has started the process to renegotiate the North American Free Trade Agreement with Mexico and Canada, both of whom are G-20 members.
Mr Trump and other critics of free trade argue that it can cause jobs, such as in the labour-intensive manufacturing sector, to move to lower-cost countries.
In a visit to Berlin ahead of the G-20 meeting, Mnuchin said the U.S.is interested in trade that is not only free but fair. Proponents say technological advances, such as automation, are more to blame for the loss of jobs in such sectors.
Trump himself insisted at a tense Washington press conference Friday, following his first meeting with German Chancellor Angela Merkel, that "I'm a free trader but also a fair trader".
Worldwide trade makes up nearly half of global economic output and officials said the issue could be revisited at a meeting of G20 leaders in July.
Conspicuous by its absence was the phrase "we will resist all forms of protectionism" that was contained in the communique from the last meeting of the group in China, July 2016.
The meeting's host, German Finance Minister Wolfgang Schaeuble, told reporters that the discussion was about "the right formulation regarding the openness of the world economy". "But it wasn't clear what one or another meant by that", he said. Its decisions don't have the same force as an worldwide treaty but simply depend on individual countries' promises to follow through on them.
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