The mayor shall supervise the conduct of all city officers and may suspend any appointive officer from office for what he shall deem sufficient cause, such suspension, however to terminate at the next regular meeting of the city council, unless such officer is, after a hearing and an opportunity to present his defense, thereupon removed from office; provided, that such meeting of the city council may be adjourned from time to time for the purpose of passing upon the right of the officer to continue office. (Prior code § 9-25)