The three people injured in yesterday's supermarket stabbing remain in a serious but stable condition, police say.
A fourth person remains in a moderate condition, Southern police district commander Paul Basham told reporters.
All four required surgery but none were in intensive care.
"This is a positive sign; however, they have a long road ahead," Basham said.
He could not say how many stab wounds the victims had, saying the matter was before the courts.
Two police officers, including one who was off-duty, were in the supermarket at the time of the stabbing and intervened.
Basham said police were today examining the scene of yesterday's attack in the Dunedin Central Countdown supermarket in Cumberland St.
He indicated the entire incident was captured on CCTV cameras.
Basham said it was early days and police would be looking into the background of the 42-year-old man accused of the stabbings. He appeared in court earlier this afternoon.
While the investigation was still in its early stages, police now had an emerging picture of what occurred yesterday afternoon.
"I'd like to recognise the Countdown staff who first intervened and were the initial victims. Members of the public then came to assist, restraining the alleged offender and providing aid and comfort to the injured.
"They all went above and beyond," said Basham.
"In this situation I think they were heroes."
Basham said every person who helped at the scene showed "tremendous bravery and courage".
He said walking away from a dangerous situation or working to "deconflict" it was the best course of action - but everyone who stepped in yesterday was a hero.
Two police officers, one of whom was off-duty, were at the supermarket at the time and also stepped in.
"The actions of those two officers helped to de-escalate the situation and minimise any further harm," said Basham.
"Other staff were on scene very quickly and feedback indicates they provided a high standard of first aid that almost certainly saved lives.
"This was an extremely fast-moving and confronting scene for our staff - they did an exceptional job when it mattered the most and I'm very proud of their efforts."
Gathering evidence at the scene was one of police's top priorities today, Basham said.
This included photography, blood sampling and collection of any discarded items for further examination.
"We've also been working to identify and speak to as many witnesses as possible, and of course, the victims who remain front of mind.
"We are currently assessing how best to support them and their whānau."
Southern DHB emergency department clinical director Dr Richard Stephenson said staff were "shocked and saddened" by yesterday's emergency.
"It's fair to say [the injuries] were significant," he said, and most victims would have ongoing issues.
The influx of patients had an "enormous" impact on hospital operations.
He was proud of the "excellent" hospital response and commended the staff who worked quickly at short notice to treat the patients.
Countdown's general manager safety, Kiri Hannifin, said yesterday's events were felt deeply across the business and the priority was supporting the injured team members, their families and the wider team.
"Today we have had counsellors on the ground and about 60 of our team have gathered together over the day to share food, a cuppa and begin the healing process together.
"The warmth and kindness shown to our team across Aotearoa by our customers, our supply partners and other businesses has meant a lot."
Meanwhile, the man who allegedly went on a stabbing rampage in a Dunedin supermarket will keep his identity under wraps until next month.
A 42-year-old man appeared in the Dunedin District Court this afternoon facing four charges of attempted murder after allegedly attacking two staff members and a married couple at the Cumberland St Countdown in the central city yesterday.
Emergency vehicles swiftly flooded the scene and the victims were rushed to the nearby hospital where they remained today.
Three are in a serious but stable state, while one is in a moderate condition.
The defendant, who was also briefly hospitalised before being discharged last night, appeared in the dock wearing a white cover-all garment, bare-footed with a white plaster on his right forearm.
He stood with his head bowed in the dock, only looking up when the judge addressed him.
Counsel John Westgate entered no plea on behalf of his client and asked for name suppression to be granted until the next appearance before the High Court in June.
Judge Peter Rollo granted the order and remanded the man in custody until that date.
He confirmed there was no formal mental-health assessment sought.
Corrections today confirmed that one of those stabbed was a staff member and it is understood his wife was also wounded.
Southern regional commissioner Ben Clark said the focus was ensuring that the staff member, their family and colleagues had all the support they need during this ''stressful and difficult time''.
Meanwhile, the son of one of those injured told the Otago Daily Times his mother's wounds were "pretty bad" and he spent yesterday by her bedside.
The man believed the mother of four - a Countdown worker - had been blind-sided during the incident but had been unable to confirm the exact sequence of events.
"She wasn't really talking much yesterday," he said.
The store manager was also understood to be among those injured.
His long-time friend Anne Coulthard told The New Zealand Herald she had worked alongside him at the beginning of his career in the late 1990s.
"I have seen and watched him grow from a young teenager to a wonderful store manager. And always looked forward to seeing him when I shopped there, we often laughed about days past when he was so much younger."
Coulthard said it was a sad day when such a tragic event happened in Dunedin.
The injured manager had previously worked at Countdown Andersons Bay in South Dunedin.
The defendant, sources told the ODT, had spent a lot of time in and around the central Dunedin supermarket.
He was such a frequent visitor staff knew him by a nickname, they said.
He is charged with killing Michelle Schiller, Jessie Currin and Glendon Currin.