FRANKFURT — American allies did not bother to conceal their annoyance Tuesday with the Trump administration’s last-minute decision to delay punitive aluminum and steel tariffs by a month, in their view leaving a sword of Damocles hanging over the global economy.

In Europe, the reprieve was seen not as an act of conciliation or generosity but instead as another 30 days of precarious limbo that will disrupt supply networks and undermine what has been an unusually strong period of growth.

European leaders, normally circumspect, are openly irritated that President Trump’s protectionist assault is aimed at them despite decades of military alliance and shared values. The region has pushed for a permanent exemption to the American trade penalties, and threatened retaliation otherwise.

They find it absurd that Mr. Trump is risking a trade war with Europe, the United States’ biggest trading partner, rather than joining forces to rein in Chinese trade practices they both oppose. And the European Union’s cautious, often ponderous approach to policymaking is now clashing directly with Mr. Trump’s unpredictability and aggressiveness.