"While I have huge sympathy for the brothers who were tragically injured in two separate incidents, it is clear there have been no substantive changes to their case since Cabinet considered the issue ten years ago."
Mr Coleman said it was not possible to distinguish between the Nepata brothers' situation and numerous others who had been injured in military service.
Maori Party MP Te Ururoa Flavell, United Future leader Peter Dunne and Maori Affairs select committee chair Tau Henare had urged Government to agree to compensation.
When the decision was announced this afternoon, Mr Henare tweeted: "Shattered, utterly shattered."
In a statement, Mr Dunne said he was deeply disappointed by the decision.
He said that the Government's implication that compensating the brothers would create a precedent was of concern, because the committee had stressed that the brothers' situation was unique.
"They fell between the cracks for adequate compensation for their injuries at the time, which created the original injustice, and today's decision, sadly, perpetuates that injustice."
Damien Nepata, from Napier, received burns to 40 per cent of his body when the Scorpion tank he was driving crashed, rolled and caught fire during training at Waiouru army camp in July 1994.
Five years earlier George Nepata, from Taupo, was paralysed in a training accident in Singapore when he was dropped head-first by the soldiers carrying him up a slope on a stretcher.