Officers were seen at the Dunedin Jewish Congregation building in George St.
A representative declined to comment when contacted by the Otago Daily Times.
Police said more than 70 organisations, including schools, hospitals, courthouses, and places of worship, had received emails.
"We know that these emails are causing real concern among members of our community, particularly the emails directed at places of worship.
"Police remain confident that the emails being received are from the same source, and are not targeted at any particular community or group."
Earlier today Auckland High Court was evacuated due to a bomb threat before 10.40am.
Outside of Auckland, the courthouse in Nelson is another location that has received the email. It was closed but has since reopened.
The New Zealand Herald understands several dozen schools have been targeted so far, including two kindergartens. The majority are on Auckland’s North Shore.
Several hospitals have been targeted, with Te Whatu Ora Health NZ revealing “some sites” received an email of concern, which they referred to police to investigate.
The emails are the same as those received by a number of organisations yesterday, including hospitals.
Helensville Primary School and Gulf Harbour School have told parents they received a bomb threat over email.
“Along with other local schools, we have just received a bomb threat,” Gulf Harbour School said.
Police are confident that the emails being received are from the same source, and do not believe there is any actual threat to the organisations receiving the emails.
Police are stationed outside at least one Auckland school, with social media posts saying three police cars with lights on were outside Waitoki School near Kaukapakapa this morning.
Auckland’s Murrays Bay Intermediate School is one of many schools that have chosen to close due to the threats.
“School is currently closed due to a threatening email. Please keep your children at home until further notice”.
Auckland’s Orewa College said due to a “health and safety” issue the school was closing immediately.
“Please follow your family emergency plan. Email to caregivers will follow shortly.”
Stella Maris Primary School also confirmed the school has received a threat and will be closed for the day.
“While it is considered a low-level threat we are erring on the side of caution. School closed today.”
Silverdale School emailed parents and advised them they kept their children at home due to the “threatening email” they received.
Police Association President Chris Cahill spoke about differentiating a hoax from a real threat with Mike Hosking on Newstalk ZB.
“Well, you know, in the past you could have taken these with a little bit of lightness perhaps and said these are just nutters, but the world’s changed dramatically, obviously in New Zealand it changed dramatically in 2019.
“So there’s got to be a really thorough threat assessment done around these things and there’s some techniques you can use.”
Cahill was tight-lipped on what those techniques are but said there are some hallmarks of a bogus threat that police look for.
“We do seem to get a lot of these around exam time.”
How difficult it is to track the perpetrators down depends on how motivated and clever they are, Cahill said.
“We’ve got some pretty good skills in this area now in our cybercrime unit... it takes some time because you use overseas servers and route things a different way, we’ve got some good partnerships overseas these days.”