An environment body in the Cook Islands, Te Ipukarea Society, says it wants the government to take action over shark finning.
Specifically, it wants a ban enforced on the use of a wire trace on longlines.
It says the use of this device means that fishing vessels are effectively targetting sharks.
The Society says the Ministry of Marine Resources should be implementing the National Plan of Action on Sharks, which already requires that fishing boats do not use wire trace.
But the Ministry's secretary Ben Ponia says their actions are consistent with the recommendations of the Western and Central Pacific Fisheries Commission.
Recently, in the Marshall Islands thousands of kilogrammes of shark carcasses and 680 kilogrammes of shark fins were confiscated from a Japanese tuna vessel.
The offending vessel - the first to be apprehended since the Marshall Islands government banned all shark fishing at the end of last year - was fined 125,000 US dollars.