Fuel pods were left at the junction of Cumsons Road and Tullygeasy Road.
The Northern Ireland Environment Agency said the waste will be removed with no harm to the environment.
Ulster Unionist Councillor David Taylor said there was  despair and palpable anger within the local community over the incident.
"This problem is now of epidemic proportion within the south Armagh area and the locations chosen by those individuals carrying out this crime, who I have no doubt have clear links to republican paramilitary elements, are very sinister indeed," he said.
"The incident in question at Cumsons Road saw the perpetrators of this crime visit the scene twice overnight to dump the fuel pods highlighting their clear disregard for those living nearby or indeed to the lawful authorities.
"As I have stated previously there is a clear desire for a co-ordinated effort to be initiated between all the relevant legal agencies to stamp out this illegal activity."
Five tonnes of waste from laundered fuel has been dumped at Newtownhamilton in south Armagh.