A water pool at a farm where two cows died of anthrax is the likely source of the disease, says Welsh Environment Minister Carwyn Jones.
The farm has been sealed off after the discovery of anthrax
Two of six cows which died at Ynys Gau farm, at Gwaelod-y-Garth, near Cardiff, were infected with the disease.
Tests are still being carried out to identify the source of the disease, but Mr Jones said vets believed it was a pool on the site.
But he said the disease was confined to the farm and was "under control".
It was confirmed on Sunday that two cows had died of anthrax at Ynys Gau farm, which also tested positive for anthrax 35 years ago.
The last case of the disease in Britain was in 2002 when a cow died at a farm in Wrexham, north Wales.
Ynys Gau farm has been sealed off, with the carcasses of the dead cows incinerated and footpaths across the farmland closed.
Restrictions will remain in place while work to identify the source continues and the remaining cattle on the farm will be monitored.
But Mr Jones said there had been progress on finding the disease source.
He said: "Vets believe they have identified the source at a particular pool on the farm.
"They are investigating whether that is the source of the outbreak and once that is confirmed, steps will be taken to deal with it."
Seven cows died of anthrax at Ynys Gau farm 35 years ago
Mr Jones said he was satisfied the anthrax was contained within the farm.
"This is a one-off incident," he said.
"We did actually have a case of anthrax in 2002 in Wrexham - it's uncommon but it does happen from time to time.
"The disease itself is on the farm rather than having been brought there from somewhere else so it is under control.
"I don't think it will spread. Nothing has moved off the form for more than a year.
"This is a disease that's contained on the farm - the risk to people is exceptionally low."
Health officials have also stressed that there is little risk to people from the anthrax outbreak on the farm.
Wales' chief veterinary officer, Dr Christianne Glossop, said the outbreak was likely to be linked to the cases at the same farm 35 years ago and that she was confident that the incident had been contained.
Dr Glossop said testing of the farmland, to identify the most likely source of infection was likely to take days rather than weeks.
Tests for anthrax on two more dead cows at the farm were negative, but farming unions have expressed concern at the outbreak.
Neil Smith of the Farmers' Union of Wales said: "The farmers will be afraid because we are still on the tail of foot-and-mouth.
"The industry hasn't recovered from foot-and-mouth yet."