Development of the facial skeleton depends on interactions between intrinsic factors in the skeletal precursors and extrinsic signals in the facial environment. Hox genes have been proposed to act cell-intrinsically in skeletogenic cranial neural crest cells (CNC) for skeletal pattern. However, Hox genes are also expressed in other facial tissues, such as the ectoderm and endoderm, suggesting that Hox genes could also regulate extrinsic signalling from non-CNC tissues. Here we study moz mutant zebrafish in which hoxa2b and hoxb2a expression is lost and the support skeleton of the second pharyngeal segment is transformed into a duplicate of the first-segment-derived jaw skeleton. By performing tissue mosaic experiments between moz(-) and wild-type embryos, we show that Moz and Hox genes function in CNC, but not in the ectoderm or endoderm, to specify the support skeleton. How then does Hox expression within CNC specify a support skeleton at the cellular level? Our fate map analysis of skeletal precursors reveals that Moz specifies a second-segment fate map in part by regulating the interaction of CNC with the first endodermal pouch (p1). Removal of p1, either by laser ablation or in the itga5(b926) mutant, reveals that p1 epithelium is required for development of the wild-type support but not the moz(-) duplicate jaw-like skeleton. We present a model in which Moz-dependent Hox expression in CNC shapes the normal support skeleton by instructing second-segment CNC to undergo skeletogenesis in response to local extrinsic signals.