President Donald Trump on Saturday threatened duties of 30% on products from Mexico and the European Union, two of America’s biggest trading partners, in an ongoing tariff campaign that’s upended global trade since he retook office in January.

The EU will suspend retaliatory tariffs on U.S. goods scheduled to take effect Monday in hopes of reaching a trade deal with the Trump administration by the end of the month.

E.U. policymakers had gradually come around to the possibility that the bloc could face 10 percent across-the-board tariffs on all goods sent to the United States, and were hoping to negotiate except...