Territory Labor has declared victory in a close by-election race sparked by the departure of former chief minister Michael Gunner, despite a swing towards the opposition and the Greens.

Chief Minister Natasha Fyles declared a win in the inner-Darwin seat of Fannie Bay for candidate Brent Potter, two and a half hours after polls closed on Saturday night.

"The constituents of Fannie Bay have been heard," Ms Fyles said.

"They want a government that backs them and only a Labor government can do that."

Mr Potter held 52 per cent of the two-party preferred vote when Labor declared victory.

On first preferences, the Country Liberal Party's (CLP) Ben Hosking was ahead with 42 per cent of the primary vote.

Labor's primary vote drops, Greens rises 

Labor's tally was 33 per cent of first preferences, with 19 per cent going to the Greens — a nine per cent jump for the minor party since the last general election.

In a short victory speech, Mr Potter thanked the Labor party and volunteers as well as Mr Gunner and the Shop, Distributive and Allied Employees' Association union.

"First and foremost to the constituents across Fannie Bay, I want to say thank you very much for believing in me," he said.

Ms Fyles brushed off questions on Saturday night about the significant drop in Labor's primary vote, which was 48.2 per cent in the 2020 election.

"I think there'll be a lot of analysis of this result over the next days and weeks," she said.

"What this is is the fourth straight election loss for Lia Finocchiaro and the CLP."

CLP says voters have sent Labor a message

Mr Hosking led on the two-party preferred count before ballots from the Parap voting centre pushed Labor over the line.

At the CLP's election night gathering, leader Lia Finocchiaro declared the result a blow to Labor and a boost for the opposition.

"It's a good night for the CLP and it's a good night for Territorians, who have clearly sent Labor a message," she said.

Ms Finocchiaro said the opposition's message — "that Labor has completely destroyed our lifestyle, and created a community where there is no community safety" — had resonated with voters. 

"We're also very encouraged by the fact that the CLP has had a six per cent swing towards it as an outcome of this election," she said.

"That sets us up for a pathway to victory in 2024."

Political debate through the campaign focused largely on crime and anti-social behaviour.

And in a seat last held by a former chief minister, the Labor and CLP candidates concentrated their campaign on hyper-local issues.

Mr Potter promised $10 million towards building the new Parap preschool, as well as extra community safety measures, including foreshore patrols and a strong voice in government.

Mr Hosking was vocal on ending the public service pay freeze, reintroducing various public drinking laws, and increasing incentives for rooftop solar.

Mr Gunner won four elections in the seat Labor has held since 1995 before announcing his resignation from politics last month.

The electorate takes in the generally wealthier inner Darwin suburbs of Fannie Bay, Parap and water-side East Point.

Voter turn-out in the seat was 68 per cent, which NT Electoral Commissioner Ian Loganathan said was surprisingly low.