This original proposal was defeated 9-2 by the council today.
Instead councillors agreed to allow council staff and the university to assess and identify a potential site for the facility on Marine Park.
The assessment will include feedback through a public consultation process.
Mason said the assessment would give council a clear picture of a potential location prior to final consideration of the long-term lease.
"When we asked the public earlier this year, the supporting responses identified the opportunity for tertiary education in marine science and engineering, along with the benefit to Tauranga as a whole."
He said the facility would not only be a significant economic development opportunity to the city, but would also provide tertiary education opportunities unique to New Zealand, "enabling young people to study courses right here in Tauranga".
The council said existing and planned activities at Marine Park would be taken into account for the new assessment.
The University of Waikato approached Tauranga City Council at the beginning of 2017 wanting to work collaboratively towards establishing an internationally sought after, multi-disciplinary research and educational facility close to the city centre at Sulphur Point.
The council identified one of the open space areas at Northern Sulphur Point as the most feasible site.
It carried out formal consultation earlier this year on the proposal to long-term lease the identified piece of land, which was at the entrance to the marina at Sulphur Point.