Police were following several lines of inquiry as they tried to track down the person responsible for the threat, posted just before midnight on Monday, acting Otago coastal area commander Inspector Mel Aitken said.
Staff and students were told by police to be alert and vigilant, but not alarmed, yesterday, a message which was reiterated today.
Police would again have a high visible presence on campus today to provide reassurance for the wider campus community, Insp Aitken said.
''We're working with Campus Watch and the North Dunedin Community Patrol to provide that reassurance.
''Some of the staff were quite upset yesterday.''
When asked if the threat was posted within New Zealand or overseas, Insp Aitken said that was forming part of the police investigation.
The post, which had now been taken down, was made by an anonymous social media user on bulletin board 4chan.
The user warned people to stay away from the university yesterday and claimed he had taken inspiration from Seung-Hui Cho, who killed 32 students and teachers at Virginia Polytechnic Institute and State University in the United States in 2007.
''If you're in Dunedin, I wouldn't recommend coming to Otago University on Wednesday,'' the post said.
''Notes have been taken from tactics used in other massacres and shootings, I know what works and what doesn't.
"The necessary preparations have been made for you to expect a shooting of a similar (possibly even greater) caliber to that of Seung-Hui Cho, who is one of my many idols.''
University of Otago associate professor in information science Hank Wolfe said yesterday there was a good chance of tracking the origin of the post and the person responsible.
"Someone like this tends to be a crackpot . . . '' Prof Wolfe said.
"They're generally not an IT [information technology] specialist.''