Consideration is given to the stationary motion of a capillary meniscus of a wetting liquid over a solid at rather slow speeds when a precursor film moved by van der Waals forces exists. A transient region between (I) the meniscus motion with a dynamic contact angle and (II) the slow-wetting regime is studied. The dependence of the dynamic contact angle on the wetting velocity is derived. The phenomenon of zero contact angle at a nonzero critical speed is demonstrated. The numerically obtained interrelation between the contact angle and the velocity is compared to that provided by the asymptotic theory. The asymptotic equations for the meniscus contact angle is shown to be highly effective over a wide range of nondimensional velocities. The meniscus contact angle existence criterion is refined. Dependence of the initial thickness of the precursor film on the speed is estimated. The conditions of the initial thickness, being in correspondence with the slow-wetting regime, are outlined.