In his opening salvo at the Group of 20 summit in Buenos Aires, Mnuchin urged China and the EU to respect "free, fair and reciprocal trade" amid talk of an escalating global trade conflict, but his French counterpart fired back that the US must "return to reason."
Mnuchin was inflexible in his approach to the EU following a series of tit-for-tat measures that began with US President Donald Trump's decision to slap tariffs on steel and aluminum imports.
"My message is pretty clear, it's the same message the president delivered at the G7: if Europe believes in free trade, we're ready to sign a free trade agreement with no tariffs, no non-tariff barriers and no subsidies. It has to be all three," said Mnuchin.
That brought a firm response from French finance and economy minister Bruno Le Maire at the G20 meeting, which brings together finance ministers and central bank governors from the world's 20 leading economies.
"We refuse to negotiate with a gun to the head," he said.
"It must be the US that takes the first step to de-escalate."
He said he expected "a change of attitude" from Trump, otherwise "there will be no choice other than to retaliate."
International Monetary Fund chief Christine Lagarde opened the summit by reiterating her fears that increasing trade restrictions would hurt global GDP.
Lagarde said that taking into account "current announced and in process measures," an IMF simulation indicates that in a worst-case scenario, a half point would be cut from global GDP, amounting to some $430 billion.
But Mnuchin showed no signs of a US willingness to back down.
Asked about Trump's threat to hammer China with punitive tariffs on the entirety of the $500 billion in goods it exports to the US, Mnuchin said: "It is definitely a realistic possibility, so I wouldn't minimize the possibility."
He added: "We share a desire to have a more balanced relationship and the balanced relationship is by us selling more goods (to China)."
Mnuchin said China must "open up their markets so we can compete fairly," although he insisted that to do so would be "a tremendous opportunity for us and a tremendous opportunity for China."
The brewing global trade conflict was always expected to dominate talks in the Argentine capital and Brazilian finance minister Eduardo Guardia said many delegates had spoken of "threats on the economic horizon" that "impact on economies, particularly emerging ones."
"Global trade cannot be based on survival of the fittest," Le Maire told AFP.
Small protests against the IMF were staged in central Buenos Aires both on the eve of the summit and on Saturday, with locals angered by a 35 percent plunge in the peso between April and June.
Argentina secured a $50 billion IMF loan in June to stabilize its economy as investor confidence in crisis-hit emerging economies sunk, with some $14 billion taken out between May and June.
"The Central Bank of Argentina has put in place measures that helped reduce financial volatility and improve transparency," said Lagarde.
Growth in the country would "stabilize in the last quarter of 2018" with a "gradual recovery in 2019 and 2020," she added.
Away from trade, Mnuchin moved to ease fears in the US that Trump would "jeopardize" Federal Reserve independence after he blasted the Fed's interest rate hikes in a television interview aired on Thursday.
"The president has made it very clear to me that he supports the Fed's independence," said Mnuchin.
Sanctions were another issue on the agenda, with Mnuchin insisting North Korea would not benefit from "relief until real progress is made" on denuclearization.
While he acknowledged the US and EU "don't see eye to eye" on Iranian sanctions, he insisted they were agreed that "Iran should never have nuclear weapons."
And he said sanctions on Venezuela were meant to "encourage better behavior" from President Nicolas Maduro's government and insisted it was "a reasonable guess" that Nicaraguan President Daniel Ortega and his allies would face penalties next.
Crypto currencies were another topic Mnuchin wanted to broach with counterparts "to make sure the G20 has proper rules and regulations so that this does not become a source and means for illicit activities."
He said: "Combatting terrorist financing is obviously a critical focus of the US Treasury and the Trump administration. We want to make sure crypto assets are not a source of that."