MPI has pointed to studies showing four out of five sea lions that entered trawl nets fitted with SLEDs would escape.
Forest and Bird and other groups and researchers have however challenged assertions that the devices, which all vessels operating in the squid fishery must use, are effective.
The environmental group was also claimed it wasn't notified of the two latest deaths at a NZ sea lion management advisory forum, held days after the week in which the sea lions were killed.
"It's a huge kick in the guts to contribute time, expertise, and expense to a specialist workshop on managing threats to the nationally critical NZ sea lion, only to find that crucial information has been withheld from us by other workshop participants," Forest and Bird marine mammal expert Katrina Goddard said.
Goddard went as far as to accuse MPI of "colluding" with and "protecting" the fishing industry - a claim that the ministry dismissed, adding that it had informed the forum of the deaths.
"MPI rejects the suggestion that it colluded with industry or anyone else to withhold the information from the Forum and Advisory Group and notes that it shared news of the captures with the Forum and Advisory Group on Friday 19 May, as part of its regular weekly update," a spokesperson said in a statement to the Herald.
"The Forum met on Tuesday and Advisory Group on Thursday and had a useful discussion about actions required to encourage recovery of the sea lion population throughout New Zealand, including at the Auckland Islands.
"These discussions are ongoing, and the timing of the update does not prevent Forest and Bird from making its views known."
MPI stated that any death of a sea lion was disappointing.
"However, while regrettable, these captures are consistent with observed capture levels in recent years and do not constitute a threat to the Auckland Islands sea lion population."
With a declining population of around 10,000, the New Zealand sea lion is the rarest sea lion species in the world and a drop in pup numbers at the Auckland Islands, its main breeding ground, spurred the fast-tracking of a threat management plan.
In the same week in which the two animals were killed, the Government this month announced it would spend $2.8 million over four years to fund further research into sea lion mortalities.
The species were also among those shortlisted by the Department of Conservation in its just-launched Threatened Species Strategy, and were sheltered by a marine mammal sanctuary stretching out to 12 nautical miles around the Auckland Islands.
Last year no sea lions were observed to be captured, and only one in 2015.
In 2014, two sea lions died after being accidentally caught by vessels operating in the southern blue whiting fishery, at Campbell Island.
Around two thirds of all sea lion pups are born at the Auckland Islands.
Last year's survey estimated 1727 pups were born on Auckland Islands, a 15 percent increase on the lowest estimate from 2009, although most of these were not expected to survive their first year.
The seafood industry, which co-manages the annual sea lion survey, has voiced its concern over sea lion deaths, also pointing to animals dying of disease and drowning in holes on the islands.
