Other prominent participants will be European Central Bank President Mario Draghi, China's finance minister, Xiao Jie, and the host finance minister, Wolfgang Schaeuble of Germany.
Angel Gurria, secretary-general of the Organization for Economic Cooperation and Development, downplayed differences over the language.
"We believe in free trade: we are one of the largest markets in the world, we are one of the largest trading partners in the world", Mnuchin said. The organization is one of several worldwide groups invited to participate in the meeting.
By contrast, last year's statement called on all G20 states to resist "all forms" of protectionism. Possible replacements include support for "fairness". The WTO operates a system of negotiated trade rules and serves as a forum for resolving disputes.
The outcome of the first face-to-face talks between Aso and Mnuchin could be a relief to Japanese officials concerned about the USA piling pressure on Japan over currency policy.
Finance ministers from the G20, which comprises more than 80 percent of the global economy, debated the wording of their final joint statement on trade at their summit in the German resort of Baden-Baden.
"We reaffirm our previous exchange rate commitments, including that we will refrain from competitive devaluations and we will not target our exchange rates for competitive purposes", the G20 said.
Trump and other critics of free trade argue that it can cause jobs, such as in the labor intensive manufacturing sector, to move to lower-cost countries.
In relation to Berlin, Mnuchin told reporters on Thursday he had listened to Schaeuble's argument that Germany's export surplus was as a outcome of the European Central Bank setting the interest rates for all 19 euro area countries.
"That's more of an issue for G20 leaders" when they meet in Hamburg in July, he said.
This year Washington wants the G20 to accommodate Trump's "America First" plan and his demand for what he describes as a fairer trading system that better reflects United States interests. Despite Mr Trump's robust rhetoric against free trade and trading partners, the new U.S. treasury secretary insisted he was more interested in solutions that avoided confrontation.
Others suggested that the G20 leaders' meeting in Hamburg this July could be the real opportunity to bring the US on board.
"Obviously he had no mandate to talk about any definitions or interpretations of what the USA administration means by "fair trade" and that is something we have to accept for the time being", Schauble said. He said, without providing specifics, that some US trade agreements need to be re-examined, while adding that, "It is not our desire to get into trade wars".