BOB Brown flew to the marginal Top End seat of Solomon yesterday claiming the Greens vote is rapidly increasing across regional Australia and is now "way ahead of the National Party".

"We have become the third political party in this country," the Greens leader said.

Senator Brown told reporters he was confident the Greens vote would be bigger in Solomon, an electorate that covers Darwin and the adjoining city of Palmerston, than in 2007 when his party's preferences allowed Labor to take the seat with a margin of fewer than 200 votes.

Greens organisers are confident the party's pledge to oppose the building of a national nuclear waste dump on a disused cattle station near Tennant Creek will boost its vote in the Northern Territory this election.

Both Labor and the Coalition support building the dump at Muckaty despite opposition from some traditional owners of the area.

"If people vote for the Greens, they will have a voice against a nuclear waste dump, and a very rigorous one at that, in the national Parliament," Senator Brown said.

Senator Brown campaigned in Darwin with well-known Aboriginal singer Warren H. Williams, the Greens' NT Senate candidate.

Bookmakers have Labor and the Country Liberals neck and neck in Solomon.

Country Liberals candidate Natasha Griggs has stirred controversy by promising the Coalition would excise land from the RAAF base in Darwin and offer more than 300 houses for sale.

The Top End has a critical shortage of affordable houses.

Labor member for Solomon Damian Hale has said Labor will relocate the houses and the land will remain part of the base.

Lingiari, the NT's other lower house seat, is expected to be held by Labor's Minister for Indigenous Health, Rural and Regional Health and Regional Services Delivery, Warren Snowdon, with bookmakers having him a favourite at $1.01 compared with $11 for Country Liberals candidate Leo Abbott.

Alice Springs-based Mr Snowdon won the seat with a 11.2 per cent margin in 2007. The seat covers 1.34 million square kilometres where 43 per cent of the population are indigenous.

Mr Snowdon has announced many funding projects for communities in the electorate, including almost $180 million for 293 school projects.