Apparatus, and an associated method, for providing a Web-based directory with automatic dialing capabilities that may be used by the user of a standard wireline or cellular telephone to establish contact with entities having SIP phones or other IP-based communication devises. The Web-based directory includes not only the names of various entities, but information on how to establish voice contact with them as well such as IP addresses or other contact numbers. A Web-based directory user establishes an Internet connection and retrieves one or more Web pages of the Web-based directory, selecting from them one or more entities from among those listed. Having made this selection, the user requests initiation of a voice-communication session, whereupon a conferencing system in communication with the Web-based directory application server initiates a call to both of the selected entity or entities using applicable communication channels and the user so that the desired voice-communication session can be established.