Mayor Charles Meeker and three other council members will look at issues related to the proposed Clarence E. Lightner Public Center.
Plans to go ahead with contruction were voted down one month ago largely because it required a tax hike.
Mary-Ann Baldwin, Bonner Gaylord and Russ Stephenson will serve with Meeker on the panel.
The task force will come up with a list of items for an independent consultant to study, such as possible sites, design, cost savings, and functionality and organization of the facility.
The independent consultant will make recommendations to the full council.
Council members voted to establish the task force after City Manager Russell Allen presented an alternate funding plan at Tuesday's meeting that would not mean a tax increase. Council members did not vote on the alternate funding plan.
The 16-story center would be located at the corner of Hargett and McDowell streets - what is currently the site of the City of Raleigh Police Department headquarters.
It would consolidate the city's public safety operations and other local government offices and functions in one location.