Upon receipt of the report of the City Manager and City Assessor, if the Council shall determine to proceed with the said improvement it shall order the said report filed with the City Clerk for public examination and shall publish notice of its intention to make the said public improvement at least once in a newspaper published and generally circulated in the City. Said notice shall describe the property to be included in the proposed special assessment district, the nature of the improvement and the estimated cost of the same, and shall set a time, not less than one week following the date of publication thereof, when the Council will meet and hear objections to the proposed improvement or to the inclusion of any property within the proposed district.