Mr Key responded by saying he understood the danger the Marshalls faced but New Zealand produced only a small amount of the world's total emissions and if it reduced its pollution levels it would have little effect on the islands.
He said most of New Zealand's emissions came from agriculture and if the country cut its primary production it could reduce its food supply or leave other markets to pick up the slack.
But the Marshalls felt New Zealand and Australia, as its "big brothers", needed to put aside their "you-go-first" attitude and show leadership in the region.
Mr de Brum told local media that New Zealand's new emissions reduction target - 5 per cent below 1990 levels - was a joke.
He toned down that criticism when speaking to the Herald, saying: "It's not to say that 5 per cent is not appreciated but I think New Zealand can do better."
He said the Marshalls and their sinking neighbours Kiribati and Tuvalu should not be seen as disposable but as the canary in the mine - what happened to them would eventually affect New Zealand too.
Asked whether his Government was considering relocation for the 55,000 residents, he said it was prudent to consider the worst case.
However, he said that some Marshallese had already shifted within the islands because of World War II, nuclear testing, and climate change, and fleeing the sinking atolls altogether was a repugnant idea to them.
Mr de Brum was born just before the first of 67 American atomic bombs were tested on the Marshalls and he compared climate change's perils to the threat of nuclear contamination.
"The parallels are obvious. We had nothing to do with the war ... yet we are the population who suffers."
Islands Forum
Who is there?
15 nations: New Zealand, Australia, Samoa, Tonga, Nauru, Palau, Vanuatu, Papua New Guinea, Marshall Islands, Kiribati, the Solomon Islands, the Cook Islands, Tuvalu, Nauru, the Federated States of Micronesia. Pacific Rim countries such as the US and China send observers to the forum.
Who's not there?
Elections in Australia mean Prime Minister Kevin Rudd will not attend. US Secretary of State John Kerry is not attending. Fiji is suspended from the forum.
What's on NZ's radar?
Discussions about Fiji's new constitution and proposed elections next year, climate change threats to microstates and initiatives for New Zealand aid to the Pacific, including renewable energy.
Sinking islands
* The Marshall Islands have a population of 55,000 spread over 180sq km of coral atolls and islands.
* 2m above sea level on average.
* Sea levels have risen 7mm a year since 1993, compared with a global average of 0.4mm.
* Sea levels are expected to increase by up to 15cm by 2030.