This paper generalizes our recent results on global robust output regulation of output feedback systems with integral input-to-state stable (iISS) inverse dynamics in two aspects. First, we consider the general relative degree case instead of the unity relative degree case. For this purpose, the one step approach proposed previously has to be generalized to a recursive approach. Second, we allow the exosystem to be uncertain. For this purpose, we need to introduce an adaptive control technique to estimate the unknown parameter vector in the exosystem. A convergence analysis of the estimated parameter vector will also be given. (C) 2013 Elsevier Ltd. All rights reserved.