Live sheep exporters are again under investigation for breaching Australia's animal welfare system, this time in Kuwait and Jordan.

The Department of Agriculture has confirmed it's investigating a complaint from Animals Australia that thousands of sheep are being sold at locations outside approved supply chains in Jordan, and some are available at the notorious Al Rai market in Kuwait, the site of previous welfare incidents.

The complaint comes on the day of the religious festival where Muslims give away meat to the poor or to family and friends.

Alison Penfold, head of the Australian Livestock Exporters Council says if the breaches are proven, there should be tough penalties.

"What disappoints me - and I'm being frank and honest here - is that exporters have to pick up the game.

"It is a real challenge to manage long and complex supply chains.

"But it is a responsibility that they have, not only under the ESCAS provisions under Australian law, but simply a responsibility if they want to continue to hold a social licence to operate."