Australia could end the disadvantage endured by its Indigenous population by opening up traditional lands as dumping sites for nuclear waste from around the world, a former prime minister, Bob Hawke, has said.

Hawke said he was confident that the answer to long-standing indigenous socioeconomic problems was to allow radioactive waste to be stored on Aboriginal land, and use the revenue to improve living standards.

Speaking at the Indigenous Garma festival in the Northern Territory, Hawke said he had met Adam Giles, the territory’s chief minister, to discuss the idea and had got a favourable response.

“We need to do something substantial to finally eliminate these disgraceful gaps in well-being and lifetime opportunities,” Hawke said. “I have no hesitation whatsoever in putting the situation in very specific terms because I believe I have the answer.

“I’ve discussed this proposal with Adam Giles, who tells me he’s been approached by a number of elders who, like himself, are keenly supportive of the proposal.”

Despite having some of the largest deposits of uranium in the world, Australia has maintained a long-standing opposition to nuclear power and storing radioactive waste from overseas.

In June, traditional Indigenous owners in Muckaty Station, north of Tennant Creek, triumphed in a seven-year battle to stop domestic nuclear waste being dumped on their land.

The site was officially nominated for radioactive dumping but four different clans claimed they had not been consulted and that the site was near a sacred area. The Northern Land Council, which made the nomination, relented amid a challenge in the federal court.

Hawke, who was prime minister between 1983 and 1991, said any nuclear waste dumping would need Indigenous leaders’ full consent, but he stressed that the solution would give Australia “the capacity for substantial new expenditure on indigenous Australians”.

He said that towards the end of his premiership in 1991, he asked the then chief scientist, Ralph Slatyer, to investigate the possibility of storing nuclear waste in remote locations in Australia.

The report found that “Australia has the safest remote geological formations in the world for this purpose, in the Northern Territory and, to some extent, in Western Australia”, Hawke said.

“Our friends in the environmental movement say the challenge of climate change is a global one requiring international co-operation, and they are right,” he said. “With Australia having the safest nuclear disposal sites in the world, we have a responsibility and obligation to make these sites available for this purpose.

“In creating a safer energy cycle for a world threatened by global warming, we would not only be doing good for the rest of the world, we would be doing enormous good for Australia as the world would pay handsomely for this service.

“In other words, we make the world a safer place, we earn an enormous amount of new money, and we use that money to help close these unacceptable gaps between Indigenous and non-Indigenous Australians.”

Dave Sweeney, a nuclear-free campaigner with the Australian Conservation Foundation, said Hawke’s proposal was a “bloody disgrace”.

“Here you’ve got a privileged white man standing up saying this rubbish should be dumped on systematically disadvantaged people’s land,” he told Guardian Australia. “It’s offensive and it’s dumb.

“For more than 20 years Aboriginal communities at multiple sites in South Australia and the NT have mobilised and defeated federal government plans for a national radioactive waste dump on their country, most recently at Muckaty. To think that they will accept an international dump is fanciful.

“To put forward that the best way to address the shameful state of the economic and structural disadvantage of the world’s oldest continuing culture is through hosting the world’s worst industrial wastes is a profound and perpetual policy failure.”

In his Garma speech, Hawke said he was “sick and tired” of the impasse in improving the fortunes of Indigenous people. He said he was saddened that he was never able to strike a treaty with Indigenous people while he was prime minister, but he said he fully supported the present move to recognise Aboriginal heritage in the constitution.