Australia will not accept high-level nuclear waste from other countries under a security pact with the US and UK.
Australia will acquire nuclear-powered submarines for $368 billion under the AUKUS agreement.
The Albanese government is introducing amendments to the bill which sets up the framework to regulate the safety of activities relating to the nuclear-powered submarines.
In response to recommendations made by a parliamentary committee, Labor has proposed changes that make clear Australia will only be responsible for high-level waste produced by its submarines.
The need to manage nuclear fuel is expected to occur in the 2050s.
The University of Melbourne's Professor Tilman Ruff, from the International Campaign to Abolish Nuclear Weapons, said the welcome move was a "relief".
"The other issue that concerns us is the proliferation potential of the fact that there is highly enriched uranium in any nuclear submarine that Australia is likely to acquire," he said.
Dr Ruff said it was "really unfortunate" the new regulator monitoring how nuclear material would be handled would sit within Defence.
"That's a fundamental conflict with good governance - the regulators should be independent," he said.
"This obviously requires very expert, but also very independent, transparent and accountable regulation."
Defence Minister Richard Marles said Labor was committed to undertaking a "robust and comprehensive approach" to regulating Australia's nuclear-powered submarine program.
"The Albanese government will continue to build the foundations to safely and securely build, maintain and operate conventionally armed, nuclear-powered submarines," he said.
Under the treaty, the US or UK can quit the pact with a year's notice.
It also requires Australia to legally protect both allies against costs or injuries arising from nuclear risks.
The agreement will remain in force until 2075 and says the AUKUS deal should not adversely affect the ability of the US and UK to "meet their respective military requirements and to not degrade their respective naval nuclear propulsion programs".
US government and military officials have moved to reassure the deal will withstand changing administrations for decades to come, amid fears it could be torn up by a new leader.
