In a city initially classified as a second-class city prior to January 1, 1993, that retained its second-class city plan of government when the city reorganized as a noncharter code city, the mayor shall be the chief executive officer of the city and shall:

(1) Have general supervision over the several departments of the city government and over all its interests;

(2) Preside over the city council when present;

(3) Once in three months, submit a general statement of the condition of the various departments and recommend to the city council such measures as the mayor deems expedient for the public health or improvement of the city, its finances or government; and

(4) Countersign all warrants and licenses, deeds, leases and contracts requiring signature issued under and by authority of the city.

If there is a vacancy in the office of mayor or the mayor is absent from the city, or is unable from any cause to discharge the duties of the office, the president of the council shall act as mayor, exercise all the powers and be subject to all the duties of the mayor.