We propose novel tree construction algorithms for multicast communication in photonic networks. Since multicast communications consume many more link resources than unicast communications, effective algorithms for route selection and wavelength assignment are required. We propose a novel tree construction algorithm, called the Weighted Steiner Tree (WST) algorithm and a variation of the WST algorithm, called the Composite Weighted Steiner Tree (CWST) algorithm. Because these algorithms are based on the Steiner Tree algorithm, link resources among source and destination pairs tend to be commonly used and link utilization ratios are improved. Because of this, these algorithms can accept many more multicast requests than other multicast tree construction algorithms based on the Dijkstra algorithm. However, under certain delay constraints, the blocking characteristics of the proposed Weighted Steiner Tree algorithm deteriorate since some light paths between source and destinations use many hops and cannot satisfy the delay constraint. In order to adapt the approach to the delay-sensitive environments, we have devised the Composite Weighted Steiner Tree algorithm comprising the Weighted Steiner Tree algorithm and the Dijkstra algorithm for use in a delay constrained environment such as an IPTV application. In this paper, we also give the results of simulation experiments which demonstrate the superiority of the proposed Composite Weighted Steiner Tree algorithm compared with the Distributed Minimum Hop Tree (DMHT) algorithm, from the viewpoint of the light-tree request blocking.