Weekly food waste collections and a second recycling bin specifically for paper and cardboard were also set to be introduced in phases across the city from April.
Mahmood said: “We remain committed to the transformation of our waste service. It has not been good enough for too long and we need to improve it.
“We are committed to creating a modern, sustainable and consistently reliable waste collection service for all residents.”
However, he went on to say the timing of the changes had been affected by the industrial dispute and would depend on “operational consideration”.
Last week, talks to resolve the strike broke down, and some drivers were put at risk of compulsory redundancy.
Mahmood said the “first priority” had been to keep the city clean and said the council’s contingency service was currently achieving a single weekly collection of mixed waste for “most households”.
He also said new waste vehicles, described as “cleaner, greener and safer”, were already being used by the council.