A move has been made to end a traditional form of fishing on the Nith estuary in Dumfries and Galloway.
Mr Dempster said fish stocks in the Nith had fallen significantly
Councillor Jim Dempster has claimed haaf-netting - introduced to Scotland by the Vikings - is damaging the salmon and sea trout stocks in the area.
He said many local anglers had contacted him about the drop in numbers on the river in Upper Nithsdale.
Now he has written to the Scottish Executive asking it to end the rights to fish the waters in this manner.
The haaf net is a sea net placed on a large frame - 18ft long by 5ft high - supported by three legs.
Fishermen walk out into shallow waters placing the frame across the current to catch the fish.
Mr Dempster believes, however, that too many fish are being taken by this method.
He said: "I would argue strongly that the overall economic benefits of rod angling to the economy through tourism and visiting anglers outweigh the economic benefit of haaf-netting.
"I am amazed at the high number of salmon being caught by haaf-netting.
"I believe firmly that this is directly related to the decreasing number of salmon being caught by anglers on the river."
Mr Dempster said it was time to consider an end to the method of fishing.
"I have come to the view that haaf-netting is actually the exploitation of salmon," he said.
"In 1962 legislation was passed to end drift netting and then in 1975 gill netting was banned.
"I'm looking for 2006/07 to be the end of haaf-netting"
Upper Nithsdale Angling Association figures show that the number of salmon caught has nearly halved in the last 20 years with sea trout down by more than 80%.