The discovery of the latest fox carcase in Tasmania's north has prompted farmers to call on their state government to increase efforts to eradicate the animals.

Tasmanian Farmers and Graziers Association chief executive officer Greg Bradfield said an established fox population would wreak havoc on the state's economy and could cost the agricultural sector up to $8 million a year.

An agricultural worker discovered the carcase on a northern midlands road last week, prompting fears the recently discovered population was gaining a foothold.

The state was believed to be fox free until a report from the Canberra-based Invasive Animals Cooperative Research Centre (IACRC) confirmed their presence in June.

Mr Bradfield said the IACRC research showed the population was still at a level where foxes could be eradicated, but the government needed to allocate sufficient resources to control them.

Gary Davies, of the Department of Primary Industries and Water, said forensic tests were being carried out on the carcase to learn "as much as possible" about the fox's origin.

Taskforce members would also conduct searches of the midlands area for evidence of other foxes.

The discovery is the fourth fox carcase to be found in Tasmania since 2001 and follows evidence of a fox killing chickens in the state's south in June.