The city assessor, if there is one, shall assess and return as provided by law all property taxable within the city, if a separate assessment district, and the assessor of the town within which the city lies shall not include in the return any property taxable in the city. Any assessor may appoint a deputy assessor as provided in section 273.06. The assessor may be compensated on a full-time or part-time basis at the option of the council, and mileage at the rate paid other city officers for each mile necessarily traveled in going to and returning from the county seat of the county to attend any meeting of the assessors of the county legally called by the county auditor, and also for each mile necessarily traveled in making the return of assessment to the proper county officer and in attending sectional meetings called by the county assessor, except when mileage is paid by the county. In addition to other compensation, the council may allow the assessor mileage at the same rate per mile as paid other city officers for each mile necessarily traveled in assessment work.