Aboriginal landowners say they will continue their fight to stop Australia's first radioactive waste dump being set up on their land.

They've again implored Resources Minister Martin Ferguson to visit Muckaty Station, near Tennant Creek in the Northern Territory, who has so far turned down repeated invitations.

Legislation setting up the waste site at Muckaty passed federal parliament's lower house last week.

Traditional owner Mark Lane Jangala arrived in Canberra on Tuesday as part of his two-pronged attack to stop the waste dump, where he is due to appeal to crossbenchers and hopefully bring them onside.

Meanwhile, his legal challenge in the Federal Court - launched on behalf of himself and other senior elders - is due to return in August.

Mr Jangala insists the radioactive waste - earmarked to be low-level nuclear waste, mostly nuclear medicines - will be devastating to the area he associates with the dreaming.

"It will not only hurt the land, but it will hurt us," said.

"We carry that land on our bodies.

"It's a very special place."

Mr Jangala has been fighting the plans since 2007 when Muckaty was first nominated as a potential site.

His lawyers are arguing he and fellow elders were ignored in the initial consultation process, with the Northern Land Council having accepted the site's nomination on the recommendation of one Aboriginal family only.