Mr Hundeyin said that a suspected cultist, aged 22, was captured on CCTV on July 7, where he allegedly was involved in the killing of a rival cult member.
The PSC said the suspension of the recruitment exercise was to resolve all contending issues with the Nigeria Police Force.
The commission also confirmed the appointment of John Amadi as a substantive Deputy Inspector General of Police ((DIG).
The mass promotion comes a few weeks after some officers threatened to embark on strike action over poor condition of service.
The PSC wants Nigerians to “raise alarm if we notice not so good persons applying to join the police.”
The PSC has consequently deferred decision on Mr Kyari’s case, while a different panel reports back within two weeks.
The ongoing exercise is to conclude the 2020 recruitment of 10,000 constables into the Nigeria Police.
Mr Kyari’s suspension was recommended on Saturday.
One dismissed officer was fired for conspiring with four others to vandalise a transformer and stealing.
Dozens of officers who were killed during thug violence in October were also promoted posthumously.
