"If they want to come back to the table and complete the deal on the terms that we were continuing to negotiate, that would be great", he said Saturday in Fukuoka, Japan, according to the New York Times.
"If not, as the president said, we'll move on with tariffs", said Mnuchin.
The comments came on the first day of the annual G-20 meeting of finance ministers from the world's biggest economies.
After the Trump administration raised tariffs to up to 25 per cent on $250 billion USA of imports from China and blacklisted telecommunications giant Huawei, China raised tariffs on rare earth exports to the U.S. and threatened to halt exports altogether.
Japan´s Finance Minister Taro Aso (C) poses next to International Monetary Fund managing director Christine Lagarde (centre L) and Bank of Japan governor Haruhiko Kuroda (centre R) during a family photo of the G20 finance ministers and central bank governors meeting in Fukuoka on June 8, 2019.
Washington has put Huawei on a blacklist that effectively bans US firms from doing business with it, and has put pressure on its allies also to shut Huawei out, arguing that Huawei could use its technology to carry out espionage for Beijing.
On his part, Mnuchin said that the meeting would be pivotal in determining the direction of the trade war.
Gurria said there was a risk of "cacophony" and a "race to the bottom" without an agreed global framework and Mnuchin agreed that "having a fragmented tax approach is not good for any of us".
"I think if we get a deal, it's a very positive thing for economic growth, for us, for China, for Europe, for the rest of the world".
If companies are still able to find a way to book profits in low tax or offshore havens, countries could then apply a global minimum tax rate to be agreed under the second pillar.
"Although I don't like them, I do appreciate the impetus for these issues", added the top United States finance official.
The representatives from Japan, US, China, France and the United Kingdom supported modifying their current regulations that allow digital giants such as Amazon, Google and Facebook to be taxed where they are headquartered, and instead implement taxes based on their revenue and number of users in every market where they operate.
The IMF warned last week that while growth was still expected to improve this year and next, the US-China tariff war could knock 0.5 percent from global GDP output in 2020, about the size of G20 member South Africa's economy. Most importantly, trade and geopolitical tensions have intensified.
"The China-U.S. issue is all you ask about".
The widening fallout from the US-China trade war has tested the resolve of the group to show a united front as investors worry if policymakers can avert a global recession.
The "main progress' will be at that meeting, Mnuchin said Saturday. It is very, very significant and we very much appreciate the commitments that Mexico has made to help us on those important immigration issues", Mr Mnuchin told reporters.