  We consider a gauged B$-$L (Baryon number minus Lepton number) extension of
the Standard Model (SM), which is anomaly free in the presence of three SM
singlet Right Handed Neutrinos (RHNs). Associated with the $U(1)_{\rm B-L}$
gauge symmetry breaking, the RHNs acquire Majorana masses and then with the
electroweak symmetry breaking, tiny Majorana masses for the SM(-like) neutrinos
are naturally generated by the seesaw mechanism. As a result of the seesaw
mechanism, the heavy mass eigenstates which are mainly composed of the
SM-singlet RHNs obtain suppressed electroweak interactions through small
mixings with the SM neutrinos. To investigate the seesaw mechanism, we study
the pair production of heavy Majorana neutrinos through the $U(1)_{\rm B-L}$
gauge boson $Z^\prime$ at the 250 GeV and 500 GeV International Linear Collider
(ILC). Considering the current and prospective future bounds on the B$-$L model
parameters from the search for a resonant $Z^\prime$ boson production at the
Large Hadron Collider (LHC), we focus on a "smoking-gun" signature of the
Majorana nature of the heavy neutrinos: a final state with a pair of same-sign,
same-flavor leptons, small missing momentum, and four hadronic jets. We
estimate the projected significance of the signature at the ILC.
