We address the system identification problem of genetic networks using noisy and correlated time series data of gene expression level measurements. Least-squares (LS) is a commonly used method for the parameter estimation in the network reconstruction problems. The LS algorithm implicitly assumes that the measurement noise is confined only to the dependent variables. However, a discrete time model for the genetic network systems will lead to serially correlated noise terms that appear in both the dependent and independent variables. A constrained total least-squares algorithm (CTLS) used in signal and image processing applications showed significant improvements in such an estimation problem over the LS and total least-squares (TLS) methods. In this paper, we propose an extended CTLS algorithm that estimates parameters for all the dependent variables simultaneously, instead of estimating them separately for each dependent variable, as in the original CTLS algorithm. In addition, the CTLS algorithm is further generalized to assign weights to the error terms according to the variances or covariances of the measurement noise. We demonstrate its improved performance over the original CTLS method, as well as the commonly used LS and TLS methods on a widely adopted artificial genetic network example, under a variety of noise conditions.