All appointive officers enumerated in this Charter whose appointments are not otherwise provided for herein shall be appointed by the Mayor and the appointments confirmed by the Council. He shall be the chief executive officer of the City. He shall have general supervision over the several departments of the city government and over all its interests; shall preside over the City Council, when present; he shall sign all ordinances passed by the City Council, if he approves of them; if he does not approve of them, he shall within eight days after their submission to him return the same to the City Comptroller’s office with his objections in writing, and at the first meeting of the City Council thereafter the same shall be entered upon their journal and they shall then reconsider such ordinance and unless two thirds of the Councilmen elected vote for its passage, it shall not become a law. If the Mayor shall not so return any ordinance within eight days, it shall become a law as if he signed it. He may call special meetings of the City Council at any time; he shall do so at the written request of four councilmen by notifying each member personally, or by written notice left at his last and usual place of abode, or his place of business during business hours, stating the purpose of such meeting. He shall countersign all warrants and licenses, deeds, leases and contracts requiring his signature, and issued under and by authority of the city.