The Northern Territory Government has written an open letter to Country Liberal Party Senator Nigel Scullion urging him to keep his word and vote against a national nuclear waste dump.

The Territory Government took out full page advertisements in weekend newspapers condemning Federal Government legislation that overrides the Territory's attempts to prevent a national nuclear waste facility.

Chief Minister Clare Martin has followed that up by signing an open letter to Senator Nigel Scullion urging him to keep a promise he made in August to cross the floor and vote against a nuclear waste dump.

"What we're doing is encouraging Territorians to let Nigel Scullion know how he should be voting," she said.

The Chief Minister says Nigel Scullion has gone back on his word.

"He said two months ago ... that he'd cross the floor, that it wasn't a great career move but he'd do this for the Territory and now we see that he's not going to do it," she said.

"He knows that his party policy is to oppose this. He knows that he's had public statements saying he will do that. Now is the time to stand up for Territorians and vote the nuclear waste legislation down."

The advertisement includes a cut out petition addressed to Ms Martin that she will forward to Senator Scullion.

The Chief Minister has been unable to provide the ABC with details of how much the newspaper advertisements will cost