Council-owned land was being investigated because of the limited availability of suitably located and sized private land.
The council has also held discussions with some owners of privately-owned commercial-zoned land in Welcome Bay.
Councillor Bill Grainger said moving to the next stage in the investigation process for a Welcome Bay supermarket was what the community had "almost been pleading for".
However, he said the community needed to know this would not happen for free and whatever site was recommended there would need to be some "trade-offs".
Aside from Councillor Catherine Stewart, the rest of the Tauranga City councillors supported moving the investigation forward.
Brownless also supported the move but said he would not vote for any future recommendation to build a supermarket on a public reserve.
Councillor Stewart said she agreed with Brownless' view.
"Any supermarket should be built on private commercial land . . . [the] council has far more important things to spend our resources on".
Community consultation by the council in 2017 revealed 66.5 per cent of people surveyed supported the potential development of one of these sites.
Councillor Robson said he supported the motion because the study had been peer-reviewed.
Once ratified by full council, the two council-owned sites and existing privately-owned commercial zone land in and next to the existing commercial centre will be assessed.
Council staff would then report back to the council in June.
The supermarket investigation will now be carried out separately to the Welcome Bay and Ōhauiti Planning Study, which is focused on addressing the challenges faced by the two communities including traffic congestion, lack of education options, retail/commercial provisions, infrastructure constraints, and the pressure from developers to enable more development.
