After ordering any improvements as provided for in section 17-917, the city council or village board of trustees may enter into a contract for the construction of such improvements in one or more contracts, but no work shall be done or contract let until notice to contractors has been published in a legal newspaper in or of general circulation in such city or village. The notice shall be published in at least two issues of such newspaper and shall state the extent of the work, and the kinds of material to be bid upon, including in such notice all kinds of material mentioned in the resolution specified in section 17-913, the amount of the engineer’s estimate of the cost of such improvements, and the time when bids will be received. The work shall be done under written contract with the lowest responsible bidder on the material selected after the bids are opened and in accordance with the requirements of the plans and specifications. The city council or village board of trustees may reject any or all bids received and advertise for new bids in accordance with this section.