On Saturday, French finance minister Bruno Le Maire called on Trump to "return to reason".
Trump's comments and policies have roiled longtime USA allies, and prompted the EU, Canada, Mexico, and others to implement retaliatory tariffs on US goods.
But those efforts will be complicated by frustration over US steel and aluminum import tariffs on the European Union and Canada.
But Moscovici said the summit that began Saturday had not been "tense", and that countries must remain "cool-headed and maintain a proper sense of perspective".
"What I stressed several times in my meetings here is that the European Union is certainly not the author of major trade imbalances", the European Union financial chief told reporters on Sunday on the sidelines of the G20 summit taking place in Buenos Aires, Argentina.
A representative for the European Council said Sunday that the USA does not necessarily need to lift steep tariffs against the European Union before trade talks can begin.
The world's two largest economies have slapped tariffs on US$34 billion worth of each other's goods so far.
U.S. Treasury Minister Steven Mnuchin has no plans for a bilateral meeting with his Chinese counterpart in Buenos Aires, a U.S official said this week. Trump on Friday threatened tariffs on all $500 billion of Chinese exports to the United States.
As reported by Reuters, the European Council sees no need for the United States to remove steel and aluminum tariffs before trade talks can proceed, continuing to keep the door open to the United States to engage in bilateral talks on trade.
Tiger Woods in contention heading into final day of The Open
McIlroy, who grew up watching Woods, said the 14-time major champion is not feared like he was during his prime. While Woods was getting off to a hot start, his fellow competitors were going the opposite direction.
Liverpool vs. Borussia Dortmund - Football Match Report
As Liverpool went all out to grab an equaliser, Jacob Larsen added a third in injury time. For Dortmund's late third goal, he was again unconvincing.
Trump to Iran: 'never, ever threaten' US again
He accused the United States of working to weaken and "overthrow" the clerical establishment and create divisions in the country. The US has provided a list of 12 demands that says Tehran needs to accept if it seeks relief from Washington's threats.
The admission was made in a joint statement agreed by all G20 members following a meeting of finance ministers in Buenos Aires, Argentina.
Meanwhile, International Monetary Fund chief Christine Lagarde has cautioned that tariff races will hinder global economic growth, warning that "in the worst case scenario" the impact will be "in the range of 0.5 percent of GDP on a global basis".
But Mr Mnuchin showed no signs of a U.S. willingness to back down. Mr Mnuchin said that, while there were some "micro" effects such as retaliation against US-produced soybeans, lobsters and bourbon, he did not believe that tariffs would keep the U.S. from achieving sustained 3 per cent growth this year.
"These include rising financial vulnerabilities, heightened trade and geopolitical tensions, global imbalances, inequality and structurally weak growth, particularly in some advanced economies", the communique said.
Mr Morrison said the ministers were very conscious of the consequences of the situation continuing.
The weekend meeting in Buenos Aires comes amid a dramatic escalation in rhetoric on both sides.
German Finance Minister Olaf Scholz said he would use the meeting to advocate for a rules-based trading system, but that expectations were low.
The U.S. tariffs will cost Germany up to 20 billion euros ($23.44 billion) in income this year, according to the head of German think-tank IMK.
"Trade protectionism benefits no one involved", he said.