In this paper, we investigate an unmanned aerial vehicle (UAV)-assisted integrated communication and localization network in emergency scenarios where a single UAV is deployed as both an airborne base station (BS) and anchor node to assist ground BSs in communication and localization services. We formulate an optimization problem to maximize the sum communication rate of all users under localization accuracy constraints by jointly optimizing the 3D position of the UAV, and communication bandwidth and power allocation of the UAV and ground BSs. To address the intractable localization accuracy constraints, we introduce a new performance metric and geometrically characterize the UAV feasible deployment region in which the localization accuracy constraints are satisfied. Accordingly, we combine Gibbs sampling (GS) and block coordinate descent (BCD) techniques to tackle the non-convex joint optimization problem. Numerical results show that the proposed method attains almost identical rate performance as the meta-heuristic benchmark method while reducing the CPU time by 89.3%.