Labor candidate Lauren Moss has claimed victory in the Northern Territory's Casuarina by-election, despite a swing to the Country Liberal Party (CLP).

With about 70 per cent of the vote counted she had a projected two-party preferred lead of 10 per cent.

She thanked family and staff as well as Labor's long-serving member for Casuarina Kon Vatskalis, whose resignation announcement in July triggered the by-election.

The results can be seen on the ABC election page.

Ms Moss, 27, had been an early favourite in the campaign, with the CLP needing a swing of more than 9.3 per cent to take what was considered a safe Labor seat.

With some votes still to be counted, there has been a swing on first preference of 17 per cent against Labor, with most votes flowing to the Greens.

The Greens did not field a candidate in the 2012 election. Its by-election candidate, Dr Michael Connard, campaigned on ending mandatory alcohol rehabilitation.

The CLP, represented by candidate Dr Harry Kypreos, improved its first preferences vote by less than one per cent.

But on the two-party preferred vote the CLP enjoyed a swing of about four per cent.

Petrol prices fuelled campaign

Ms Moss, a small business owner, campaigned on lowering the NT's petrol prices, saying they should be tackled by supporting an independent retailer and introducing a mobile phone app with up-to-date petrol price information.

She also fought Federal Government moves to increase the fuel excise.

Despite her win, however, the result may ultimately be seen as a hollow victory for Labor.

The party suffered a large swing, despite the CLP being under pressure following the retirement of former deputy chief minister Dave Tollner, who made homophobic comments.

Dr Kypreos was a member of the local Greek community, a group that has a strong presence in Casuarina.

He caused a storm early in the campaign by bringing to public attention a little-used act of parliament he said could be used by the Government to force down petrol prices.

However, he later threw his support behind the CLP's endorsed measures - a fuel disclosure bill and petrol price summit.