They also recommended council request HBRIC provide advice on the implications of shelving, or withdrawing from the scheme, and on steps "if any exist" that could progress the scheme.
Although this advice had not been received, yesterday the mood among councillors was clear, with the majority advocating for council to shelve the dam and focus on other priorities.
"Let's be very clear, for all practical purposes this project is over," councillor Peter Beaven said.
"I feel like we've got a dying beast in front of us that we've got to euthanise."
Napier councillor Neil Kirton said there no ambiguity about the Supreme Court's ruling, and although council could look at other scenarios "the reality is, it's all over".
"It deserves to be shelved, to at least preserve the intellectual property that is invested in the dam, some $20m. We owe it to the ratepayers to ensure that that possibility is on the shelf, but the reality is that the dam is dead."
A review into the scheme completed this year found withdrawing from it could cost a write-down of about $19.5m already invested.
The five anti-dam councillors at the meeting also discussed how other projects, and challenges before council could now become a higher priority with the dam shelved.
However Central Hawke's Bay councillor Debbie Hewitt - whose constituency was said to have the highest need for water storage - urged her fellow councillors to "pause", reminding them yesterday's discussion was just about the suspension of RWSS work.
"The Supreme Court decision ... was an absolute tragedy for the people of Central Hawke's Bay, for the wider community, and the [RWSS] project at large."
However with "$20m on the table" council needed to wait for advice from HBRIC before making any further rules about the project, or what could be considered to secure access to the land.
This was echoed by pro-dam councillors Alan Dick and Fenton Wilson.
There were two possible avenues which could allow the swap to go ahead in future - a legislation change, and securing access to the land through the Public Works Act.
Neither of these seemed palatable - Mr Beaven said the possible two-year wait for a legislation change could require so many elements of the scheme to be renegotiated that the dam would become "a completely new project".
The committee later agreed five-four to his recommendation that council express to HBRIC it would not support obtaining the land by compulsory acquisition under the Public Works Act.
The Supreme Court ruling last week marked the end of a lengthy and controversial battle through the courts that began in 2015.
