Genomic sequencing was conducted to see if the Auckland strain of the virus was similar to cases linked to the Melbourne site.
Bloomfield said on Tuesday a final report into that possible route of transmission through chilled surfaces would be completed shortly"but it seems clear now that the possibility is being ruled out from that investigation".
The chief executive of Americold for Australia and New Zealand Richard Winnall,who had already saidno containers had been sent from Melbourne to Mt Wellington,said the company was pleased a link had been ruled out.
"We believe this is the right decision and will give confidence to consumers and the temperature-controlled logistics industry,"he said.
The country now has 90 active cases of coronavirus,including 69 in the Auckland cluster,20 in returned travellers and one other community case.
According to genomic sequencing results,that one separate case is a man who worked as a maintenance worker at a Rydges Hotel managed isolation facility in Auckland and is not linked to the cluster.