He said there were still many in the community who believed a city of Tauranga's size needed somewhere to store and display its taonga.
"I wanted to signal to the community that the conversation about the museum is something we need to keep alive."
He said the funding would be used to bring stakeholders together to continue the debate.
Councillor Catherine Stewart, who voted against funding the museum, called for the funding to be pulled out of next year's draft budget.
"We have heard these discussions for the last 10 years."
She said the council needed to find other ways of displaying the city's collection of heritage objects.
The council will continue its discussions about the draft Annual Plan in 2019.