All contracts for the construction of any work pursuant to sections 17-530 to 17-532, or any portion of such work, shall be let to the lowest responsible bidder, and upon not less than twenty days’ published notice of the terms and conditions upon which the contract is to be let having been given by publication in a legal newspaper in or of general circulation in such city or village. In all cases the city council or village board of trustees shall have the right to reject any and all bids that may not be satisfactory.