The identification of biological parameters governing dynamics of Genetic Regulatory Networks (GRN) poses a problem of com-binatorial explosion, since the possibilities of parameter instantiation are numerous even for small networks. In this paper, we propose to adapt LTL model checking algorithms to infer biological parameters from biological properties given as LTL formulas. In order to reduce the combinatorial explosion, we represent all the dynamics with one parametric model, so that all GRN dynamics simply result from all eligible parameter instantiations. LTL model checking algorithms are adapted by postponing the parameter instantiation as far as possible. Our approach is implemented within the SPuTNIk tool.