The dispersion relation for circularly polarized electromagnetic waves in a warm two‐component plasma subject to parallel static electric and magnetic fields has been derived from the linearized coupled Boltzmann‐Maxwell equations with the collision frequency assumed to be independent of the particle velocity. The effect of a weak longitudinal electrostatic field,E0, on the propagation characteristic of the right‐ and left‐hand circularly polarized waves in an isothermal electron‐proton plasma is examined in detail and illustrated numerically for a conveniently chosen set of the system parameters. For the right‐hand polarized wave the electrostatic field effect is found to be significant for a wave with frequency &ohgr; in the vicinity of the electron cyclotron frequency&ohgr;z≡ (eB0/m). For example, for a given &ohgr; and &dgr; ≡(eE0/mc&ohgr;) > 0an increase in &dgr;, or inE0, leads to the increase or decrease of the attenuation constant &agr;, of the wave according to whetherY ≡ (&ohgr;z/&ohgr;) < 1 or Y > 1. Moreover, forY = 1.10, when &dgr; < 0 (i.e., whenE0and the wave vectorkare oppositely directed) &agr; increases with |&dgr;|. On the other hand, when &dgr; > 0 an increase in |&dgr;| causes &agr; to decrease and for a sufficiently large value of &dgr;, &agr; may become negative so that the wave may experience a spatial growth.