  We examine the existence of semimetallic spin-density wave states in iron
pnictides. In the experimentally observed metallic spin-density wave state, the
symmetry-protected Dirac cones are located away from the Fermi surface giving
rise to tiny pockets and there are also additional Fermi pockets such as one
around $\Gamma$. We find that the location of a pair of Dirac points with
respect to the Fermi surface exhibits significant sensitivity to the orbital
splitting between the $d_{xz}$ and $d_{yz}$ orbitals. Besides, in the presence
of orbital splitting, the Fermi pockets not associated with the Dirac cones,
can be suppressed so that a semimetallic spin-density wave state can be
realized. We explain these finding in terms of difference in the slopes and
orbital contents of the bands which form the Dirac cone, and obtain the
necessary conditions dependent on these two and other parameters for the
coexisting Dirac semimetallic and spin-density wave states. Additionally, the
topologically protected edge states are studied in the ribbon geometry when the
same are oriented either along $x$ or $y$ axes.
