(a) The mayor of the city shall be its chief executive officer and conservator of its peace. It shall be his or her special duty to cause the ordinances and regulations of the city to be faithfully and constantly obeyed.

(b) The mayor shall:

(1) Supervise the conduct of all the officers of the city, examine the grounds of all reasonable complaints made against them, and cause all their violations of duty or other neglect to be properly punished or reported to the proper tribunal for correction;

(2) Have and exercise the power conferred on sheriffs, within the city limits, to suppress disorder and keep the peace; and

(3) Perform such other duties compatible with the nature of his or her office as the city council may from time to time require.

(c) The mayor shall report, within the first ninety (90) days of each year and at such other times as he or she shall deem expedient, to the council the municipal affairs of the city and recommend such measures as may seem advisable.

(d) (1) In addition to the powers and duties already pertaining to that office, the mayor of any city of the first class shall be clothed with and exercise and perform the following:

(A) A mayor may veto within five (5) days, Sundays excepted, after the action of the city council thereon, any ordinance, resolution, or order adopted or made by the council, or any part thereof, which in his or her judgment is contrary to the public interest; and

(B)

(i) In case of a veto, before the next regular meeting of the council, the mayor shall file in the office of the city clerk, to be laid before that meeting, a written statement of his or her reasons for so doing.

(ii) An ordinance, an order, or a resolution or part thereof, vetoed by the mayor is invalid unless, after the written statement is laid before it, the council, by a vote of two-thirds (2/3) of all the council members elected thereto, passes it over the veto.

(2) The mayor does not have the power of veto in circumstances prescribed under § 14-43-501(a) or § 14-43-411(a).