 In 2005, Mavrokefalidis' contribution during the FIBA Under-21 World Cup was very significant, as Mavrokefalidis greatly helped the Under-21 Greek National Basketball Team win the silver medal, after losing to Lithuania by just two points in the gold medal game.A year later, in 2006, the senior men's Greek national basketball team head coach Panagiotis Giannakis became impressed by the Mavrokefalidis' abilities and called him to participate in the Greek basketball senior men's training camp, one month before the 2006 FIBA World Championship took place in Japan.However, as he was selected in the 2006 NBA draft by the Minnesota Timberwolves, Mavrokefalidis informed the coach shortly before the outset of the World Championship that he had decided to go back to Minnesota and participate in performance improvement training camps, and thus he lost the team's 12th man roster place to Sofoklis Schortsanitis.