NSW Deputy Premier John Barilaro confirmed the delay in COVID exposure site announcements for Batemans Bay was primarily because individuals had been uncooperative with health staff.
Mr Barilaro said on Wednesday the case was "really complex".
"Individuals aren't being cooperative, I can't say any more than that," he said.
Mr Barilaro said the lack of cooperation was the sole reason announcements about exposure sites in the South Coast haven of Batemans Bay had been delayed.
"The level of movement that occurred, no registration of where they had been, not cooperative in relation to telling us their movements or who they may have been in contact with and that makes it very, very difficult," he said.
"Everything has been tried here, and it's very difficult to get people to tell the truth. We rely on people to be honest."
Mr Barilaro said there was action NSW Health could take to ensure people cooperated with contact tracers.
"The NSW Chief Health Officer Dr Kerry Chant has powers that can put people into quarantine, get the police involved and there are penalties for not being cooperative," he said.
Since the first case was announced on Monday, no exposure sites have been released and Mr Barilaro said he understood the delay caused anxieties in the community.
"The only other case we've got at this stage is a close contact, and I genuinely mean a very close contact, of the first case," he said.
"This means just maybe there hasn't been any other exposures, but it's still early days. You've got to wait for the full 14 days to be clear of that and that's probably the only thing that gives us a bit of hope."
NSW Health was continuing to work with the positive case and more information was expected this afternoon.
In the meantime, NSW Health is urging anyone with symptoms to get tested as soon as possible.