The repository was to have been built on a sheep farm acquired for the purpose near Woomera in South Australia, but after years of wrangling with state authorities, Prime Minister John Howard said his government had dropped the plan.
The decision came after Howard's Liberal colleagues expressed fears over the electoral implications of foisting the dump on South Australia in which three key marginal seats are under threat at the election due by the end of this year.
Howard blamed a recent Federal Court ruling against the forced acquisition of the land and the failure of the states to cooperate with Canberra in finding a national solution.
He handed responsibility for waste storage back to the states, saying they had all accepted the need for safe and secure disposal, "but no-one wants it in their back yard."
He said the national government was committed to taking responsibility for its own low-level radioactive waste and would try to find a suitable site, by going offshore if necessary, to one of the hundreds of islands dotted around the coast.
"We'll conduct a search to see if we can find some Commonwealth (Federal Australian) land either onshore or offshore and we'll put the Commonwealth low-level waste there," he said.
But he warned the states that if they were refusing to cooperate, and adopting a "destructive attitude", then he would thrust back on them the responsibility for looking after their own waste.
"If they want to play sovereign state politics, not-in-my-state politics, okay, they can do that, but they will have to look after their own waste."
Howard's proposal was attacked by the Labor opposition as a desperate attempt to solve the nuclear waste problem by creating "Pacific solution II" -- a reference to the so-called Pacific solution by which unwanted asylum seekers were shipped to Pacific islands.
"The very idea of storing nuclear waste on a Pacific atoll or in a country like Nauru is dangerously ridiculous and ought be condemned," said shadow industry minister, Senator Kim Carr.
"Export of Australian waste to Pacific Forum countries is prohibited by international treaty.
He said that just as Australia did not want to be the dumping ground for waste from other countries, "nor should we be exporting our waste to others. We have a responsibility to store our own radioactive waste.
"We generate it, we have to clean it up, we have to look after it."
Howard's conservative government purchased the South Australian land over the objections of the Labor-controlled state government, the land's owner and local Aboriginal communities.
The state government appealed against the acquisition and the Federal Court upheld the appeal, finding there was no "urgent necessity for the acquisition".
It rejected federal government arguments that it would have been contrary to public interest for the purchase to be delayed.