We study the quark spectrum at nonzero temperature and density near the
critical point (CP) of the chiral phase transition incorporating effects of the
scalar- and pseudoscalar-density fluctuations in a chiral effective model with
a nonzero current quark mass. It is known that the soft mode associated with
the second-order transition at the CP lies in the spacelike region of the
scalar-density fluctuation. We find that the soft mode influences the quark
spectrum significantly near the CP, resulting in the shift of the quasiquark
peak. Effects of the composite stable pions on the quark spectrum near the CP
are also discussed.