At a hearing in Invercargill this week, Environment Southland staff made a submission that the new rules should replace the existing temporary controlled area notice that has been in place there since 2017.
The recommendation was prompted by the discovery of a further spread of Undaria pinnatifida in the sound.
Speaking after the submission, biosecurity and biodiversity operations manager Ali Meade said the joint-agency response team identified that Undaria had spread outside the currently covered controlled area, but still remains contained to Breaksea Sound.
"It is disappointing to see the spread. However, it's very important that we don't give up, as efforts are still being made to control it."
The regional council, Biosecurity New Zealand, Department of Conservation and Fiordland Marine Guardians were devising a management plan for the pest.
If implemented, the rules would place the onus on boaties moving in and out of Breaksea Sound to ensure their boats and gear were free from Undaria contamination, and support enforcement of anybody found in breach of the rules.
Undaria is an invasive Asian seaweed first discovered in New Zealand waters in 1987.
Submissions, including staff responses, on the proposal for a Southland regional pest management plan were heard by the hearing panel in the past months.
The panel is likely to deliberate before making recommendations to council on the final plan.
