Police have so far declined to comment on the nature of the threat.
"While we understand people want to know the specific nature of the threat, at this stage of our inquiries we cannot provide this detail as it could compromise the outcome of the investigation.
This is a complex investigation and it's important we have the opportunity to work through it systematically and thoroughly," Southern District Commander Paul Basham said.
The "specific and detailed" threat led the university to abandon two graduation ceremonies on Wednesday and Otago Polytechnic to postpone graduation ceremonies scheduled for today and pre-grad ceremonies yesterday and today.
Prof Hayne today acknowledged the decision would incredibly disappointing and for that some this was their third attempt to graduate.
"My heart goes out to you all. This has been a difficult decision and I hope that you will find ways to celebrate.
"The depth of feeling has been only too real over the previous few days. No one deserved this, particularly the young people from the University and Polytech who were expecting to celebrate their graduations at the Town Hall this week," Prof Hayne said
Police had advised all on-campus events are able to continue.
This included all graduation events like Māori pre-graduation, which would go ahead. Graduands would be able to pick up their certificates and details about this would be sent directly to graduands.
As with Wednesday's graduations that were postponed, the university would plan for a replacement ceremony for tomorrow's graduations for 2021.
Currently, next week's graduations ceremonies on Wednesday 16 December and Saturday 19 December will go ahead as planned.
Professor Hayne said one "huge positive" she was taking from this week was the incredible strength and resilience of the tertiary community in North Dunedin.
"In particular, the students have been incredibly magnanimous and have taken care of each other and their friends and whānau.
She also acknowledged police.
"Their community support and expert guidance has been excellent, and I cannot thank them enough.
"We will continue to work with the police. As you will understand, I cannot comment on any matters related to this ongoing case."
In a statement last night, Southern District Commander Paul Basham said while he understood people wanted to know the nature of the threat, at this stage releasing details could compromise the outcome of the investigation.
"This is a complex investigation and it's important we have the opportunity to work through it systematically and thoroughly.
"The safety of our community remains our priority and we continue with our two-pronged approach — an active investigation and an increased police presence in the city."
He encouraged anyone with information to contact police.
Massey University lecturer in security studies Dr Rhys Ball, a former New Zealand Security Intelligence Service (NZSIS) officer, said the university and police were right to be "erring on the side of caution" in how they treated the threat.
It had come in the wake of several terrorism-related events in this country and overseas, so the police had to assume a worst-case scenario.
Dr Ball said he was not surprised the police and university had withheld knowledge of the threat for at least a day before postponing Wednesday's ceremonies.
"That gives you 24 hours to work out where the threat has emanated from, and if it's legitimate."
Giving a warning or a threat before carrying out an act of violence was not normal, but the history of terrorism had many examples of it, such as by the Provisional Irish Republican Army in the 1970s and 1980s.
"It depends on the motivation for actually carrying out an act of violence."
The rise of electronic communication meant security threats were much easier to make than in the past, and therefore they happened more frequently.
"But you have to treat each one as legitimate and serious until it becomes clear otherwise that it's not.
"To get it wrong is unacceptable."
While it was normal for any organisation handling a security threat to keep information close to their chest, he thought it unlikely the police would deliberately deceive the public by saying they had not identified who made a threat when in fact they did, "because it might come back to bite you".
Otago Polytechnic said yesterday it had made the "devastating" decision to postpone graduation and pre-grad ceremonies scheduled for yesterday and today, affecting 1150 graduands, after following advice from police.
Otago Polytechnic chief executive Dr Megan Gibbons said the safety of students and staff was its "number one priority".
It was working on rescheduling events for next year.
Otago University Students' Association president Jack Manning said graduating students were naturally disappointed by Wednesday's postponements because it was a day they had been working towards for years.
"This is the culmination of years of hard work and sacrifice," Manning said.
"But that said, we will show resilience — maybe it's something in the water, maybe it's the events of this year."
That was shown by how many had celebrated the occasion anyway, with hundreds walking around the university campus on Wednesday with their families and having their photos taken.
However, there would be some for whom the postponements would be harder to accept.
"That feeling is also very valid — people handle things differently."
A free counselling service was available, through Student Support Services, for anyone who needed help, he said.
