Ponter has given a notice of motion for the council's sustainable transport committee meeting on Wednesday.
It invites the regional council Chief Executive to engage with the Wellington Airport Company and bus operators on public transport options to and from the airport.
The motion comes after the airport chief executive Steve Sanderson sent a letter to the regional council in June, weighing in on Let's Get Wellington Moving.
The $6.4b package includes a new mass rapid transit spine to the airport but is at least five years away.
In the letter, Sanderson said 6.4 million travellers passed through Wellington Airport last year, with the majority journeying via the Mt Victoria tunnel and Basin Reserve.
It said they are in favour of public transport to the airport, but in their view and experience it must be fast, direct and reliable.
"Motorists will benefit from good and affordable public transport links because this will encourage some drivers to leave their cars at home and free up road capacity,
"We look forward to accommodating mass public transit with light rail or trackless trams."
Ponter's motion said the Flyer was unlikely to make any significant dent in mode shift for airport users with its current price structure, lack of visibility on the Metlink network and lack of immediate presence at the airport.
It said it was imperative the council started working with the airport to see what options could be put in place as a forerunner to mass transit.
"The airport's calling for more access into the city but the airport's also got to do its part and that part is about encouraging people to move from taxis, Ubers and private cars and on to public transport to reduce the amount of congestion we have on our roads," Ponter said.
It's understood the contract between the airport and NZ Bus ends in 2020.
Ponter said it was integral to have a public transport option to the airport if the Flyer did stop.
NZ Bus Chief Commercial Officer Scott Thorne said they were committed to continue operating the Flyer service.
He said it provides a "valuable service and a positive alternative to taxis."
"The driver shortage has impacted performance of the service this year, but we expect that to be resolved in the near future."