Speaking at the Geneva Motor Show in Switzerland, Sergio Marchionne said: "I'm suggesting that we stop playing tit-for-tat, that we get our blood pressure to go back down to normal (and) that we sit down at the table and find a way to resolve this issue."
"I don't think we have to escalate this into a full-blown trade war," he added.
An intensifying war of words between the EU and the U.S. began on Thursday when Trump announced plans to slap hefty tariffs on steel and aluminum imports. He said "very stupid" trade deals had allowed countries from all over the world to take advantage of the world's largest economy.
That prompted a firm response from the U.S.' trading partners, as well as criticism from the International Monetary Fund (IMF) and the World Trade Organization (WTO).
Shortly after the U.S. president's full-throated backing of tariffs, EU trade chiefs were thought to be considering whether or not to impose a 25 percent tax on around $3.5 billion of U.S. imports, Reuters reported.
European Commission President Jean-Claude Juncker had previously vowed to react firmly to Trump's tariff threats.
"If the E.U. wants to further increase their already massive tariffs and barriers on U.S. companies doing business there, we will simply apply a tax on their cars which freely pour into the U.S.," Trump said on Twitter.
Marchionne explained that Trump clearly feels it would be "wrong" for the U.S. to continue with the current trade deal. "Let's take him seriously on that issue and that concern," he said.