SEOUL—China’s detention of a 9-year-old girl and six other North Koreans who tried to escape their country has triggered a public outcry here for South Korea’s president, while pursuing peace talks, to confront Pyongyang about rights abuses.

“How long will you look the other way?” read a sign held by a family member of the detainees at a May 1 rally in front of South Korea’s presidential Blue House.

Chinese...