Mueller led the 81st Infantry Division into its first combat on September 17, 1944 during the Palau Islands campaign. While the majority of the 81st Division invaded Angaur Island, the 321st Regimental Combat Team (321st RCT) joined the 1st Marine Division in its assault of Peleliu Island. The 321st RCT also assisted in capturing Ngesebus Island, Kongauru and Garakayo Islands. Operating under a naval task force, the 323rd RCT occupied Ulithi Atoll.