The decision marked a temporary reprieve from what would have been a sizable escalation in Trump's multi-front trade wars.
The US tariffs threaten a major chunk of global economic activity with profound disruption. Hundreds of billions of dollars' worth of cars are manufactured, shipped and sold internationally every year.
In a proclamation, the president directed US Trade Representative Robert Lighthizer to update him within 180 days on the outcome of negotiations with the EU, Japan and "any other country" Lighthizer deems appropriate.
By leaving the threat of tariffs hanging, Trump's move raises the temperature in European capitals already angered by the imposition of punishing US duties on steel and aluminium last year.
Trump's decision also preserved a truce declared last year with European Commission President Jean-Claude Juncker in which both sides agreed to cease trade hostilities while efforts continued to resolve the trade dispute.