This paper presents a multiport implementation of the time-domain-vector-fitting algorithm (TD-VF) for achieving a common-pole rational model approximation from simulated time-domain responses. Similar to the frequency-domain counterpart of the algorithm, a fast realization of TD-VF is achieved based on QR-factorization with consideration of sparsity. The computational speed is further increased by an adaptive downsampling procedure which removes rows from the system matrices. The required model order is reduced by low-pass filtering the input responses, giving a model that is essentially free of spurious Gibbs-like oscillations. The resulting model is directly compatible with Electromagnetic Transients Program-type simulation programs. The multiport TD-VF is applied for the calculation of a frequency-dependent network equivalent (FDNE) of two subnetworks: a 24-kV distribution system and a 145-kV regional transmission system. We show that the procedure offers advantages by achieving faster simulations and reduced memory requirements. In addition, the procedure often enables the use of a shorter time-step length than with the detailed subnetwork representation, thereby achieving further reductions in computational time.