"But we reserve our rights to be protectionists to the extent that we believe that trade is not free and fair".
After two days of talks in a 12th century Norman castle, many delegations expressed a measure of relief.
"We are excited about USA trade policies and I think you probably saw we made an announcement of a 100-day economic plan with the Chinese so I think we're very happy with how we're proceeding with the Chinese", the former banker said.
"We are agreed on many things. including on the fight against cyber crime which is unfortunately very timely", Padoan said on his arrival for Sunday's closing session.
G7 finance ministers and central bank governors attending a two-day meeting in Italy have said they want a better sense of the plans of U.S. President Donald Trump, who has threatened to upset the global consensus of recent decades on issues such as trade and rules for the financial services industry.
Mnuchin's brand of diplomacy had already showed signs of evolution between that meeting and one in Washington a month later, with his position that trade be "fair" rather than "free" crystallizing into a call for "reciprocal free trade". Earlier, he told reporters that "the relationship with Mnuchin improves every time we see each other".
As growing protectionism is feared under the administration of US President Donald Trump, the statement skipped any explicit wording on protectionism, as did a statement issued by Group of 20 finance chiefs in March.
The G20's reference to trade said only that they were "working to strengthen the contribution of trade to our economies".
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Italian Economy Minister Pier Carlo Padoan, the G7 host, said Trump's plan to slash taxes on businesses was "ambitious" and he was keen to hear more about it from Mnuchin.
United States Treasury Secretary Steven Mnuchin, center, smiles as he takes a walk in the Puglian town of Bari, southern Italy, which is hosting a G7 of Finance Ministers and Central Bank Governors meeting, Thursday, May 11.
The China deal came just months after Trump was attacking Beijing in an election campaign in which he promised to restore trade barriers if he felt they were needed to protect United States interests.
Already, Trump has yanked the United States out of the 12-nation Trans Pacific trade agreement and threatened to pull out of its NAFTA agreement with Canada and Mexico.
"We must not backpedal on free trade as it has contributed to economic prosperity", Aso said.
"There is not enough clarity yet", said International Monetary Fund chief Christine Lagarde after the working breakfast.
Others topics for discussion have included strengthening cybersecurity, reaching an agreement on worldwide tax rules, and countering terrorism financing.
Asked how pro-active the U.S. delegation had been on the first day of the G7, France's Sapin said they had been "quite discreet in their presence", and he appeared to take a swipe at Trump's frequent use of Twitter. "We're going to try to get this done as quickly as we can".