Labor is claiming victory in the Queensland seat of Lilley, but the Australian Electoral Commission still says its one of three seats too close to call.
The latest results show Prime Minister Scott Morrison with a one-seat majority of 76 seats, with two other seats in doubt but leaning towards Liberal on Monday afternoon.
Labor has 66 seats, with the possibility of 67, and there are six crossbenchers.
The retiring Wayne Swan left his seat of Lilley to be contested by first-time Labor candidate Anika Wells, who claimed victory on Monday.
"We didn't take this for granted for a single hour, and it turns out every single hour mattered," she told the ABC.
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Labor is relying on ABC election analyst Antony Green's election calculator, which has called the seat for Ms Wells.
More than 13,000 votes remain to be counted, and Ms Wells is ahead by 840 votes.
The AEC hopes to be in a position to declare the first official results of the federal election early this week, with votes counted over the weekend.
The commission says a number of the 151 House of Representative seats will require a full distribution of preferences before a result can be declared.
The NSW seat of Macquarie is now down to a margin of 39 votes, with Liberal candidate Sarah Richards ahead of Labor incumbent Susan Templeman.
The AEC website shows about 90 per cent of votes had been counted by Monday evening.
The Tasmanian seat of Bass is also too close to call with almost 92 per cent of the vote counted.
Liberal candidate Bridget Archer has a lead of 701 votes over Labor incumbent Ross Hart on a two-candidate preferred basis.
In the upper house, the coalition looks set to control 34 or 35 seats after the half Senate election, still short of 39 seats needed for a majority.
However, it will likely have a smaller crossbench of six senators to deal with, down from 10 when the current Senate ends on June 30.
