President Donald Trump set a two-month deadline for the European Union to implement a trade deal with the U.S., before he increases tariffs to “much higher levels.”

A federal trade court ruled President Trump didn’t have the authority to impose new global tariffs after a previous set of levies was struck down by the Supreme Court in February.

The EU’s implementation of the deal has been slowed by tensions over other tariff threats by Trump, including disputes linked to his bid to annex Greenland, as well as legal uncertainty following a US...