Tohoshinki, a South Korean male pop group of five hugely popular in their home country, Japan and other parts of Asia, will suspend their performances, their Japanese agency Avex Management announced Saturday. An agency source said after consultations with the members—Jejung, Changmin, Junsu, Yunho and Yunchun—that each of the five has decided to pursue his own dreams and direction. The group, also known by its Chinese name acronym TVXQ, debuted in South Korea in 2004 as a teen unit. The five made their Japan debut the following year and had No. 1 hits such as ‘‘Purple Line’’ and ‘‘Mirotic.’’ Rumors have circulated that the group would disband after a conflict between some of the members and their Korean agency. In Japan, they have appeared in the ‘‘Kohaku Utagassen’’ annual New Year’s Eve TV music extravaganza for the last two years. Jejung is set to appear in a Japanese TV drama series starting this month.