In the late 1970s, radioactive material from atomic weapons tests done 30 years prior was dumped into a 100-metre wide bomb crater and then covered with concrete.
It was the site of the largest nuclear clean-up in United States history.
The Marshall Island's Red Cross Secretary-General Jack Niedenthal said the site is still highly radioactive and locals want the waste gone.
"No one would ever tolerate this in their back yard. There's a very serious situation up there, but we just can't seem to get anyone to pay attention to it."
He said it should never have been allowed as a permanent solution.
"They put all this material in the hole and they covered it in cement and to them, I know, to the United States, that was a permanent operation, turnkey, they left, they're gone, it's not their problem anymore. I mean that's really the way they look at it."
Environmental radiation expert David Krofcheck said he agreed something had to be done but it was an issue of who would do it.
"The best long-term solution would be to elevate it, move it someplace but I don't know who's going to do that. I can see the Americans possibly coming back and patching it but I can't actually see them importing 80,000 cubic meters of radioactive waste from weapons tests into the United States."
He said the most likely courses of action were patching the cracks in the dome with concrete or doing nothing at all.
He said it was not ideal, but it was almost certain that the waste would end up in the Pacific Ocean.
"This material will get diluted as it spreads out, the ocean is vast and the only thing that will save us is that vastness. So as it dilutes, hopefully the levels will be so low that it will be not the problem that it is today in its concentrated form in this repository.
"I don't see any other immediate practical options."
He said cleaning up radioactive waste could be done, and was being done in Japan after the Fukushima disaster.
"It can be done but we're talking about a place in the middle of the Pacific, a small place that no one has ever heard of really, in the United States I'm sure and it concerns us because we live in the Pacific."
He said the threat of rising sea levels may encourage the United States to take action but he was not optimistic.
"It's mostly an American mess so the Americans should do this, but realistically I don't see any other option other than letting it diffuse and letting the planet take care of itself."
Dr Krofcheck said New Zealand waters were not at risk because the ocean currents were taking the waste towards China and the Philippines.
Photo: AFP / US DEPARTMENT OF ENERGY The cloud from an experimental thermonuclear device or H-bomb on Elugelab Island in the Enewetak atoll in 1952.