And Mr Woodhead has previously warned that wallabies, already present in large numbers in South Canterbury, represent a major strategic threat to Otago farming and the environment.
A report tabled at yesterday's meeting of the council's regulatory committee said about 10,000ha of land was inspected for wallabies during a recent reporting period.
Several reported wallaby deaths and sightings had also been investigated, including a dead animal found east of Duntroon which appeared to have been shot and dumped on the side of the road.
Staff had also followed up a report of a wallaby sighting in North Otago.
''The investigation found that other land owners have seen the animal over the past few months and have failed to report to the ORC,'' the committee report said.
Night inspections with thermal imagery were continuing in the area.
Mr Woodhead said it was ''critical'' that any sightings of wallabies were promptly reported to the ORC.
Wallaby hunting was available in South Canterbury and it was vital that wallabies were prevented from establishing themselves in Otago, he said.
The council warned last year that anyone found deliberately releasing wallabies in Otago, which would be in breach of the Biosecurity Act, could be imprisoned for up to five years, and/or fined up to $100,000.