At the Southern Squid Trawl Fishery, which surrounds the Auckland Islands 465km south of Bluff, there is an allowance of 38 deaths of the nationally vulnerable animals per year before the Government will take action.
Two weeks ago, the sixth observed death there this year was recorded by the Ministry for Primary Industries.
While speaking at the New Zealand Marine Sciences Conference in Dunedin yesterday, Ms Sage said she supported a zero bycatch policy.
After the conference she said it was ''unacceptable'' there were six deaths this year and that there was a 38-death allowance before the fishery was closed.
''We wouldn't accept this number of deaths if they were kakapo.''
''More vessels are now being visited by fishery bycatch liaison officers, who work with vessel operators to develop fit-for-purpose strategies to reduce bycatch in their operations, such as through the construction and deployment of bird scaring lines.''
Ms Sage did not respond to a question of whether she had pushed for zero bycatch to become Government policy.
Forest and Bird marine conservation advocate Katrina Goddard said it was ''great'' the minister expressed support for the policy publicly.
''That's the sort of leadership we need.''
The organisation has been pushing for a zero bycatch policy.
''Our position is pretty clear. We know fishing is not the only issue with sea lions, but it's one that we can manage.
''It's an ambitious goal, but it's about driving down that number.''
Ms Sage yesterday also announced a $350,000 project to test devices which set baited hooks underwater, out of the sight and diving depth of seabirds.
This would help to save declining albatross species, she said.
The device will soon be tested in Nelson.