Levy said 'customer revolution' was required to get Aucklanders back onto public transport - with improvements needed to park and ride facilities, bus shelters and timetables.
"We need to change almost everything we do, re-frame everything we do to actually deliver on frequency and precision. We need to have a total re-look at pricing, which must be attractive and appealing. It's a total change.''
Veolia's contract to operate Auckland's passenger rail network runs out in June 2016, but Levy called for major improvements in the next 18 to 24 months.
"We can't afford for this to drag on. So they need the opportunity to respond to this. It's a very different relationship now.''
Veolia chief operating officer Martin Kearney said they had made huge improvements to the rail network in recent years.
"I won't tell you that we're perfect but I'll tell you that we're striving for continuous improvement.''
He was confident Veolia would continue to operate Auckland's trains, and said the company also wanted to be considered to run the City Rail Link.
Auckland Chamber of Commerce chief executive Michael Barnett said Auckland Transport should carefully consider its options.
"When you have a look at the usage by Aucklanders of our public transport system at the moment it's not particularly high and there must be a reason for that.
"[Auckland Transport] have got a provider, Veolia, and they've got a product and if the product isn't attractive to customers then they've either going to change the product or change the provider. If I was sitting in Lester Levy's seat, I would be looking at both.''
Labour Party Auckland issues spokesman Phil Twyford agreed.
"If Auckland Transport could cut out the middleman and provide a better, more convenient service at a reduced cost, Aucklanders would thank them for it and would start using rail in droves.
"What's holding back patrons at the moment is poor levels of service and, to be quite honest, the tickets are just too expensive. If they were to find efficiencies and reduce the cost, a hell of a lot more people would take the train or bus to work.''
Levy said it was feasible for Auckland Transport to run the trains on its own, but any changeover would be disruptive.