North Korea and Malaysia slapped exit bans on each other’s citizens, escalating more than a week of tit-for-tat retaliation between once-friendly nations in the wake of an investigation into the killing of Kim Jong Nam on Malaysian soil.

On Tuesday morning, Pyongyang said it had barred all Malaysian citizens in North Korea from departing the country until officials could ensure that the safety of North Korean diplomats and citizens in Malaysia was “fully guaranteed through the fair settlement of the case that occurred in Malaysia,”...