Traditional owners of the land earmarked for a nuclear waste dump in the Northern Territory remain divided on the plan, despite another location for the dump being put forward.

Dianne Stokes, an elder with the Yapa Yapa people from Muckaty Station, was one of about 20 traditional owners who met with the Northern Land Council (NLC) and federal government on Wednesday.

She told AAP that one of the five Aboriginal clans that formed part of the Muckaty Land Trust continued to support the proposed waste dump, but other clans were opposed.

Because songlines and dreamings crossed clan boundaries, though, a unanimous agreement should be needed for the nuclear dump to go ahead, she said.

"We have got our dreamings and they don't go in a straight line like a highway; they criss-cross," Ms Stokes said after the meeting.

"It is very hard to have one group saying yes and the other groups saying no."

The waste dump was originally planned to be built in South Australia, but local opposition saw the federal government seek to relocate the proposed facility to the NT, a jurisdiction seen as constitutionally less likely to successfully fight it.

A site at Muckaty Station, about 110km north of Tennant Creek, was flagged as a possible site but Federal Court action is under way from some traditional owners who wish to have it put elsewhere.

This week the NLC revealed it would commence consultations with traditional owners over a second site at Muckaty.

Ms Stokes said she was unhappy with Wednesday's meeting because none of the traditional owners was given a detailed map of where the dump was to be located, although some were driven to the site, which is about 20-30km northwest of the first site at Muckaty.

On Wednesday the NT Chief Minister Terry Mills reiterated his support for the nuclear dump.

Labor's local MP for the area covering Muckaty, Gerry McCarthy, criticised Mr Mills' comments.

"We have fought long and hard against it, emphasising the decision must be based on best-practice science, and after less than three months in government, Terry Mills has decided to support it," Mr McCarthy said.