BRUSSELS—European foreign ministers, unnerved by the election of Donald Trump as president, plan to huddle on how to handle relations with the U.S. over key issues like Russia and Iran at an emergency dinner called for Sunday night.

The European Union worked closely with the Obama administration to construct broad economic pressure against Russia over the Ukraine crisis and strike an agreement with Iran to scale back its nuclear program. During the presidential campaign, Mr. Trump suggested he could upend his predecessor’s...