Recycling centres in Armagh City, Banbridge and Craigavon will not be reopening.
The decision was taken after party leaders on council discussed the issue with officers this afternoon.
Both the DUP and the SDLP had advocated reopening the facilities as an “essential service”
But this was not backed or voted through.
DUP Group Leader Councillor Mark Baxter said he was “disappointed” at the decision.
He had indicated phased opening would have helped alleviate problems but this not go ahead.
SDLP Group leader Thomas O’Hanlon also voiced annoyance.
The meeting came after dozens of bags of rubbish were left the gates of the recycling centre in Keady.
He said: “The SDLP proposed that a managed and phased re-opening of the centres should begin immediately given the huge demand from the public, but also out of concern for public health.
“We proposed the possibility of putting in place a managed process in place across a number main recycling centres. We argued that these facilities by their nature would lend themselves to implementing social distancing measures that would protect both council staff and the public whilst sites were operational.
“However, this was not agreed by all parties.
“At present, the advice from the NI Executive is that people should only be making essential journeys, and there are a number of essential services listed that should remain open.
“We are awaiting revised guidance from the Assembly and have asked officials to engage with Departmental Officials to have recycling deemed as an essential service.
Mr O’Hanlon said the situation was being “kept under constant review” and urged people in the interim to refrain from dumping rubbish and to “act responsibly”.