Techniques for supporting positioning for terminals in a wireless network are described. In an aspect, positioning may be supported by a location server that can reside in different entities. In one design, the location server may obtain positioning information (e.g., measurements) for a target device via a common positioning protocol. The location server may use the common positioning protocol regardless of where it resides and may communicate with other entities via this protocol. The location server may determine location information (e.g., a location estimate) for the target device based on the positioning information. In another aspect, positioning may be supported by transporting multiple positioning messages together. In yet another aspect, positioning may be supported by transporting a positioning message containing multiple parts defined by different organizations. In yet another aspect, positioning may be supported with shared measurement data units and/or shared assistance data units that may be applicable for different positioning methods.