The federal government wants to build a national radioactive waste dump about 110km north of Tennant Creek.

Some indigenous groups are challenging the plan in the Federal Court.

Minister Gary Gray met with about 40 Aboriginal people against the proposed waste site on Thursday.

Dianne Stokes, an elder with the Yapa Yapa people from Muckaty Station, told him they don't want waste at Muckaty.

"It's beautiful country and will be ruined if the dump goes ahead," Ms Stokes said.

One of the five Aboriginal clans support the proposed waste dump but the other clans are opposed.

A spokesman for Mr Gray said the minister was on a "listening tour" and paid the traditional owners a visit while travelling through the NT on other business.

Muckaty Station was nominated as a site by the Northern Land Council in 2007.

But since then several traditional owners have argued they were not properly consulted and did not give their consent.

The matter will return to the Federal Court in Melbourne on August 14 for a directions hearing.