ENVIRONMENTALISTS and opposition politicians are criticising the Northern Territory government after Chief Minister Terry Mills appeared to accept a nuclear waste dump would be built in the jurisdiction.

"I accept the premise of this, that there needs to be a site," Mr Mills has told ABC radio.

"Given that, we then need to make sure that the territory is properly advantaged and benefits from the decision that we are forced to wear on behalf of the country, and that it is done safely, and they are my primary concerns," he said.

The former Labor government in the Northern Territory had opposed the planned dump, which is to be located at Muckaty Station, about 120km north of Tennant Creek.

Originally, a site at Woomera in South Australia was named as the best site for the nuclear waste dump, but local opposition forced the site to be moved.

Lacking the status of a state, the NT was less able to fight plans by the federal government for the plan.

On the weekend, Mr Mills met with federal Resources Minister Martin Ferguson, the minister responsible for the project.

Although some traditional owners had accepted the site at Muckaty, a Federal Court case brought by other indigenous people from the area opposed to its planned location is under way.

The Northern Land Council (NLC) has revealed that a secondary site at Muckaty was now under consideration and formal consultations regarding it would begin this week.

"The proposed additional nomination is a separate proposal to that made by the NLC in 2007, and concerns a different area of land on Muckaty Station," NLC chairman Wali Wunungmurra said in a statement on Tuesday.

The Labor Party opposition criticised the NT government's announcement.

"Terry Mills is rolling over to Canberra and not standing up for territorians who have great concerns about the impact a nuclear waste dump will have for generations," said the ALP's Gerry McCarthy.

"News that there is now another site being nominated in the same region is extremely concerning," said Mr McCarthy, MP for the electorate that includes Muckaty.

Nuclear-free campaigner at the NT Environment Centre, Cat Beaton, said her group was outraged at the latest comments from Mr Mills.

"We were very disappointed for him to say we should accept a waste dump," Ms Beaton told AAP.