Prime Minister Scott Morrison could have a team of up to 78 MPs in the lower house, giving him the chance to appoint a Speaker and govern in majority.
The Australian Electoral Commission says counting of postal votes would be under way in all 151 seats on Tuesday, having initially prioritised postal votes in Boothby, Chisholm, Cowan, Macquarie and Wentworth.
But the focus will be on three particularly close contests in which the coalition is in the lead.
Liberals' Sarah Richards edged ahead of Labor MP Susan Templeman in the NSW seat of Macquarie on Monday, with the AEC website showing there were just 50 votes separating the pair in the evening.
The Liberals also appeared on track to win the Labor-held seats of Chisholm in Victoria and Bass in Tasmania.
In Bass, the Liberals' Bridget Archer sits on 50.3 per cent of the two-party vote, ahead of incumbent Labor MP Ross Hart.
Liberal candidate for Chisholm Gladys Liu holds 50.4 per cent of the vote, ahead of Labor's Jennifer Yang.
If the current count trends continue, this will give the Liberals 78 seats in the 151-seat House of Representatives, with Labor on 67 and six crossbenchers.
In the previous parliament the numbers were: Liberals 58, Nationals 16, Labor 69, Greens 1, Centre Alliance 1, Katter's Australian Party 1, independents 4.
Australian Associated Press