Meanwhile, the Tumed Mongols began moving into the Kokonor region (modern Qinghai), raiding the Ming Chinese frontier and even as far as the suburbs of Beijing under Altan Khan (1507–1582). Klieger writes that Altan Khan's presence in the west effectively reduced Ming influence and contact with Tibet. After Altan Khan made peace with the Ming dynasty in 1571, he invited the third hierarch of the Gelug—Sönam Gyatso (1543–1588)—to meet him in Amdo (modern Qinghai) in 1578, where he accidentally bestowed him and his two predecessors with the title of Dalai Lama—"Ocean Teacher". The full title was "Dalai Lama Vajradhara", "Vajradhara" meaning "Holder of the Thunderbolt" in Sanskrit. Victoria Huckenpahler notes that Vajradhara is considered by Buddhists to be the primordial Buddha of limitless and all-pervasive beneficial qualities, a being that "represents the ultimate aspect of enlightenment." Goldstein writes that Sönam Gyatso also enhanced Altan Khan's standing by granting him the title "king of religion, majestic purity". Rawski writes that the Dalai Lama officially recognized Altan Khan as the "Protector of the Faith".

What region did the Tumed Mongols move into?