A trade war is now a reality, French Finance Minister Bruno Le Maire has warned as G20 ministers gather for a summit in Argentina.
The current US trade policy of imposing unilateral tariffs is based on "the law of the jungle", he said.
But US Treasury Secretary Steven Mnuchin defended the tariffs and urged the EU and China to open their markets to allow free competition.
Last week, US President Donald Trump described the EU as a foe on trade.
Mr Trump later threatened to impose tariffs on all $500bn (£380bn) of Chinese goods entering the US in a growing trade row.
The US has large trade deficits with both the 28-member EU and China.
The two-day talks in Buenos Aires bring together finance ministers and central bankers of the world's top 20 economies.
What did the French minister say?
"World trade cannot base itself on the law of the jungle and the unilateral increase of tariffs is the law of the jungle," Mr Le Maire told AFP news agency.
"The law of the jungle, the law of the fittest, this cannot be the future of global trade relations.
"The law of the jungle will only turn out losers, it will weaken growth, threaten the most fragile countries and have disastrous political consequences," Mr Le Maire said.
He added that a trade war was now a reality, and that the EU could not consider negotiating a free trade deal with the US without America first withdrawing its tariffs on steel and aluminium.
What about Mr Mnuchin's comments? The US treasury secretary backed President Trump's stance on trade with the EU and China, saying they both need to open their markets.
"My message is pretty clear, it's the same message the president delivered at the G7 (last month in Canada): 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," he said.
Turning to China, Mr Mnuchin warned punitive tariffs against Beijing were "a realistic possibility".
"We've been very clear with our objectives," he added.
How has the tariffs row worsened?
On 1 June, the Trump administration introduced tariffs of 25% on steel and 10% on aluminium imported into the US.
Mr Trump argues that global oversupply of steel and aluminium, driven by China, threatens American producers, which are vital to the US.
The US president believes that if you have a trade deficit - if you import more than you export - you are losing out.
The EU later introduced retaliatory tariffs on a range of US goods, including bourbon whiskey, Harley Davidson motorcycles and orange juice.
On China, Mr Trump warned earlier this week he was ready to slap tariffs on all imports from the country.
Last week, Washington listed $200bn worth of additional Chinese products it intends to place tariffs on as soon as September.
The list named more than 6,000 items including food products, minerals and consumer goods such as handbags, to be subject to a 10% tariff.
It is still under public consultation, to last until the end of August.
The US and China have already imposed tit-for-tat tariffs of $34bn on each other's goods.