A new method is developed for deriving first order density corrections to gas transport coefficients using the time correlation function formalism. In a moderately dense gas, both kinetic and potential contributions to the flux are significant. This article extends the projection operator technique developed in our previous work for purely kinetic flux operators [J. Chem. Phys. 109, 3452 (1998)] to include the effects of the potential contribution to the flux. The method introduces two projection operators, one for each of the kinetic and potential flux contributions, with the consequence that the calculation of a transport coefficient involves a matrix associated with the two flux contributions, and the inversion of this matrix. The binary collision expansion of the resolvent in each of the matrix elements allows a transport coefficient at moderate gas densities to be expressed in terms of integrals over functions of the intermolecular potential. In the following article, it is shown that these results are consistent (that is, within a similar level of approximation of the integrals) with the known density corrections for the coefficients of viscosity and thermal conductivity.