Those tests were cancelled until further notice, the board said.
Alternative arrangements had been made for funeral directors and other mortuary users.
Asbestos fibres were also found in several areas used only by staff on the third, fourth, and fifth floors of the clinical services building, in laboratories, clinic rooms, changing rooms and corridors.
No asbestos was present in the air, tests showed.
Swab testing revealed asbestos dust in the waiting area next to the ultrasound suite, in three radiologists' offices, and in a corridor.
Communication over the issue was confused yesterday.
Chief executive Carole Heatly told media at a press conference that patients were unaffected, because ultrasound equipment could still be used.
But a union contacted the Otago Daily Times shortly afterwards to advise that was incorrect, and there was significant disruption, which the board subsequently admitted.
The press conference at Dunedin Hospital yesterday was fronted by Ms Heatly, commissioner Kathy Grant, occupational hygienist Andre Halkyard, surgical division medical director Stephen Packer and occupational and environmental medicine authority Associate Prof David McBride.
A senior communications manager has been flown in from the Canterbury District Health Board to co-ordinate the board's public response.
Mr Halkyard, of Precise Consulting and Laboratory, said it was not known how long the asbestos had been present on the surfaces of the affected areas, and it was not known how it got there. It may have been disrupted during maintenance or other work.
Asked if pregnant women could have been exposed while waiting for an ultrasound, Prof McBride said the risk was ''negligible''.
Prof McBride said the risk was greatest to hospital maintenance staff.
The risk to other staff was very low to negligible, he said.
Ms Heatly said air testing had been done regularly over the past few years.
As far as she knew, swab testing had not been carried out previously.
She said staff were handling the situation well, doing everything possible to minimise disruption to patients.
''My message to the public is we are doing everything we can to manage the risks we are aware of.
''We will continue to test and, if we find any other areas that are positive, we will be really pro-active and we will isolate and close down those areas.''
All the asbestos fibres found were white asbestos.
The new finds follow tests, confirmed earlier this month, that revealed damaged asbestos in ceiling cavities above non-public areas in the clinical services building, lecture theatre block and the Fraser Building.