The interactions and orientational correlations of charged rodlike colloidal particles in a salt-free suspension are calculated using an "ab initio" approach which combines molecular dynamics for the rods and classical density functional theory for the counterions. Both fluid and liquid-crystalline phases are investigated. It is found that the interaction between charged rods can satisfactorily be described by an effective Yukawa-segment model which in general differs, however, from the Derjaguin-Landau-Verwey-Overbeek segment model. For strongly interacting long rods, an exactly soluble Yukawa-segment model, based on a cylindrical Poisson-Boltumann cell, is proposed which reproduces the ab initio data quite well in the liquid-crystalline phase.