A novel algorithm for the identification of genetic networks from gene expression data is presented. Our approach is based on an ordinary differential equations (ODE) model of the network, and on an assumption of linearity around an equilibrium point of the cell machinery. Here we start by describing the application of NIR (Network Identification by multiple Regression) to a state-of-the-art in silico gene expression dataset provided by the Dialogue for Reverse Engineering Assessment and Methods 2 (DREAM2) reverse-engineering competition (challenge 4). Then we present NIRest (NIR with perturbation Estimate), a tool that builds upon the original NIR and extends its use to cases in which the generating perturbations are not known. The remarkable results obtained with in silico datasets support the validity of NIR and NIRest assumptions and the effectiveness of our approach. Comparison with other leading methods based on Bayesian networks and mutual information shows the performance advantage of NIRest, which at the same time provides directed and undirected versions of the inferred network and an estimate of the mode of action.