Labor is ahead in the polls for Lingiari, but it could still be weeks before an official result is declared.
As of Tuesday morning, Labor's Marion Scrymgour had a slim lead against the Country Liberal Party's candidate Damien Ryan of 51.27 per cent to Mr Ryan's 48.73 per cent on a two party preferred basis.
In other words, Ms Scrymgour has just over 1000 more primary votes than Mr Ryan.
The ABC's election analysts have called Lingiari in favour of Labor. However, there are yet to be any official claims of victory or defeat from either candidate.
Australian Electoral Officer for the Northern Territory, Geoff Bloom, said there were still a few thousand votes to be counted over what was expected to be a two-week process.
"What we've counted already for Lingiari, and for Solomon for that matter, is all of the House of Representative ballot papers that came to us from the static polling places, from the early voting centres, and from the mobile teams, including the remote area mobile teams," Mr Bloom said.
"What we haven't counted is votes that come from the declaration votes - so declaration votes [are] the ballot papers inside an envelope."
These declaration votes include outstanding postal votes, votes cast by Territorians in another part of the Territory or interstate and telephone votes cast by Territorians between Thursday and Saturday last week.
He said the AEC doesn't physically have these votes yet, and is set to begin receiving and counting them over this and next week.
"There's many 1000s of envelopes that have not been counted," he said.
Although the seat has been called by some analysts for Labor, Mr Bloom said the AEC is not prepared to make the call until all the votes have been counted.
"I know some of the parties and the analysts are saying yes, they're already calling it for Labor. But we certainly couldn't do that. It is way too early for us to do that," he said.
"What happens when we count these declaration votes? We simply don't know. Will the margin tighten up? Will it drift out even further? We just don't know."
Greens candidate Blair McFarland was the third most popular candidate in Lingiari with 11 per cent of the primary vote, followed by Tim Gallard for Pauline Hanson's One Nation party with 5 per cent.
On election night, retiring former Lingiari MP Warren Snowdon told the Katherine Times Labor was feeling hopeful but not getting ahead of themselves.
"I'm hopeful. I wouldn't overstate it but we're in a good position," he said.
"We expected a swing against us which has happened, but we've done well."
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