Direct numerical simulations (DNSs) of rotating turbulent Poiseuille flows are performed to study the effects of both cyclonic and anticyclonic system rotation on the kinematics of the quasi-streamwise vortices. By using the second invariant of the deformation tensor, a number of streamwise vortices are detected and averaged in the wall vicinity where the intense sweep motion, i.e., the inrush motion of high-speed fluid toward the wall, is related to the quasi-streamwise vortices. The effects of the system rotation on the angle of vortex axis are clearly observed as studied in longitudinal vortices of the homogeneous shear flow. Moreover, by calculating the probability of the emergence of the counterclockwise vortices (CCVs) around a clockwise vortex (CV), we find that with increase in the anticyclonic system rotation, the probability increases and decreases in the ejection and sweep sides of a CV, respectively. In contrast, cyclonic system rotation attenuates CCVs in both sides of a CV, though it increases at the top of the CV. This distribution of CCVs is found to affect sweep motion related to the quasi-streamwise vortices.