However, Fisheries Minister Shane Jones said they will not "be panicked or intimidated by loud, shrill voices" and he had no intention of changing the rules around fishing in the areas where the species habitat.
Māui and Hector's Dolphin Defenders chairwoman Christine Rose will promote events in Invercargill on February 10 and 11 to raise awareness about the issue.
The species were only found in New Zealand and there were about only 40 Hector's dolphins in Otago and about 200 in Southland, they were at risk to be extinct if things continues to operate in the way it was, she said.
"They had being wiped out by the fishing industry in trawl and set nets, and no dolphin should be killed in a fishing net.
"Thousands have been killed since industrial fishing, and 17 since the Prime Minister Christopher Luxon took office, so we're calling for protection for the dolphins throughout their range, and that's out to about 100 metres deep or 20 nautical miles, so they are prevented from becoming extinct."
Ms Rose said there was a record number of reported deaths of dolphin in recent times.
However she believed these huge numbers were always there but not reported, until the roll out of cameras on boats.
"Cameras on boats are revealing their worth, exposing the true impacts of the fishing industry.
"At the moment, if a fishing boat kills Hector's dolphins, they either don't have to take any action at all, or ... they can say, `well, we're not going to fish in this area for the next month' and then a month later, they can go back into that same area and kill dolphins again.
"So we're saying that there needs to be permanent bans, and that's been backed up by the world authorities on dolphin and whale conservation, such as the International Whaling Commission and the International Union for the Conservation of Nature."
She said the group would also take the United States government to court, through the Court of International Trade, because they continues to import fish from the New Zealand's Māui and Hector's dolphin fisheries, even though their Marine Mammal Protection Act stated they must prohibit imports from fisheries from countries that did not meet their by-catch standards.
She approached the Prime Minister, Conservation Minister Tama Potaka and Mr Jones and they "basically say that it's OK to kill 50 Hector's dolphins a year", she said.
"How they think that's acceptable, because the people of New Zealand certainly don't think it's acceptable, and the people of the world don't think it's acceptable."
Speaking to the Southland Express, Mr Jones said there had already been litigations in the US courts and this was very costly as New Zealand's exports took a blow of several million dollars.
"There has been a huge catastrophisation around Māui's dolphin ... There are thousands of Hector's dolphins all around the South Island.
"And I think the majority of South Islanders are worried about income, maintaining jobs. And they want the government to take a balanced approach and not be panicked or intimidated by loud, shrill voices from the NGO sector.
"I think any proposals that this group might have to litigate against New Zealand's economic interests in foreign courts is very negative and it has the effect of undermining our economic sovereignty."
He said there were mitigation measures in place and he believed people across the country appreciated that the fishing industry was big part of the country's export and employed many New Zealand families.
"No-one goes out deliberately targeting a dolphin ... but it's a wildlife industry and from time to time, things don't work out as intended.
"They are part of the natural environment and they are one of the elements that we manage in relation to the fishing industry, but I have no intention of closing any part of the fishing industry down."
A protest will be held on Oreti Beach on February 10 at noon following by a public meeting on February 11 from 6pm at Invercargill City Library meeting rooms.