SEOUL—South Korea’s president is trying—and so far failing—to rally European support for loosening sanctions on North Korea, a move that also risks putting him further at odds with the Trump administration’s efforts to maintain pressure on Pyongyang.

Following rapidly thawing relations between Seoul and Pyongyang this year, South Korean President Moon Jae-in is appealing to European leaders during a nine-day trip through Paris, Rome and Vatican City, Brussels and Copenhagen to boost engagement with North Korea.