“(But) the next 48 hours remains critical and I ask all Tasmanians in the south to work together to get on top of this as quickly as we can.”
There were more than 1,400 tests collected in the past day, a record for Tasmania.
The lockdown was sparked by a 31-year-old man who has refused to co-operate with contact tracers after being arrested in Hobart’s northern suburbs on Tuesday.
He earlier absconded from the city’s Travelodge hotel and spent 18 hours in the community, including two houses, a Woolworths supermarket and a park.
His list of primary contacts had jumped to 158 people, as of Saturday morning. Forty of those people have so far returned negative tests.
Mr Gutwein previously described the behaviour of the man, who arrived on Monday night without a border pass, as outrageous.
About 70 people came into contact with the man at the Bridgewater Woolworths on Tuesday afternoon.
People must remain at home unless shopping for food and essential supplies, exercise within a 5km radius of their house, or for medical appointments or COVID-19 tests or vaccinations.
Other exemptions exist, including for the provision of compassionate care.
Face masks must be worn outside the home, while cafes, restaurants and hotels are only allowed to serve takeaway, and a host of businesses have closed.
The man has been confirmed as having the Delta variant of the virus.
Extra testing and vaccination clinics have been rolled out in Hobart’s northern suburbs, where rates are lagging.
Tasmania has just one other active case, a 15-year-old boy who flouted home quarantine rules in Launceston earlier this month.
On the back of tough border measures, the state has recorded just three cases this year.
Meanwhile, Queensland is declaring all of southern Tasmania a COVID-19 hotspot. From 1am Sunday, anyone arriving into Queensland from the locked-down areas will need to go into hotel quarantine.