In this work, we pose the problem of gene regulatory function identification using a new general framework based on function separation. We prove the uniqueness of the solution within this framework in an almost always sense. Additionally, we develop an iterative scheme, called iterative function separation (IFS), which is guaranteed to converge to a solution. Both these results together guarantee the computation of the unique solution. We also develop theoretical limits on the number of gene expression level measurements (time samples) sufficient to uniquely reconstruct the network. The proposed method (IFS) is validated using synthetic networks both within and outside of the modeling domain of the new framework.