Abstract.We have investigated the role that the transverse electric field of the laser plays in the acceleration of electrons in a laser wakefield accelerator (LWFA) operating in the quasi-blowout regime through particle-in-cell code simulations. In order to ensure that longitudinal compression and/or transverse focusing of the laser pulse is not needed before the wake can self-trap the plasma electrons, we have employed the ionization injection technique. Furthermore, the plasma density is varied such that at the lowest densities, the laser pulse occupies only a fraction of the first wavelength of the wake oscillation (the accelerating bucket), whereas at the highest density, the same duration laser pulse fills the entire first bucket. Although the trapped electrons execute betatron oscillations due to the ion column in all cases, at the lowest plasma density they do not interact with the laser field and the energy gain is all due to the longitudinal wakefield. However, as the density is increased, there can be a significant contribution to the maximum energy due to direct laser acceleration (DLA) of those electrons that undergo betatron motion in the plane of the polarization of the laser pulse. Eventually, DLA can be the dominant energy gain mechanism over acceleration due to the longitudinal field at the highest densities.