Prime Minister Anthony Albanese looks set to form a majority Labor government.
The ABC election computer is projecting that Labor will hold at least 76 seats — the minimum required to form a majority government.
The ABC projects Labor will secure the Melbourne seat of Macnamara with MP Josh Burns being re-elected.
Mr Burns defeated Liberal Party candidate Colleen Harkin on two-party preferred, but faced a strong challenge from the Greens' Steph Hodgins-May, who finished second on first preference.
The seats of Deakin and Gilmore remain in doubt.
Mr Albanese was sworn in to office last week, after it became clear Labor would govern in either majority or minority.
He was able to assure the Governor-General that Labor was the only major party able to form a stable government, allowing him to head to Tokyo for a meeting with world leaders.
Given the Coalition was so far behind on the seat count, having lost heartland seats to teal independents, it was practically impossible the Coalition could use the crossbench to form a minority government.
Labor will need to supply a Speaker in the House of Representatives, removing a vote from its side of the aisle. But the Speaker has a casting vote in the event of a rare tie.
The new government is confident it could have passed its legislation in the Lower House without a majority, given the size of the crossbench.
The crossbench will have 16 members, with an ideological spectrum that ranges from Queenslander Bob Katter on the right to the Greens on the left.
It is likely, sources have suggested, that the new government will strike deals with the teals, independents and Greens to strengthen the passage of its legislation.
The latest Senate results show Labor will need the Greens, and potentially either Tasmanian Jacqui Lambie or incoming ACT senator David Pocock, to pass legislation.
Labor still needs to find a new deputy leader in the Senate to replace Kristina Keneally, who failed in her bid to move to the Lower House.
There is pressure on the Right faction to put forward a woman to ensure the upper and lower houses' leadership is gender-balanced.
But that will have implications for Mr Albanese's cabinet because there are no women in the Right faction on the frontbench in the Senate now Ms Keneally is gone.
The Labor caucus will determine who will serve in the cabinet when it meets on Tuesday.
The proportion of Left and Right members on the frontbench will be determined based on how many seats each faction wins.
The party is also under pressure to reward Western Australia, which sealed Labor's victory.
Mr Albanese is also keen to ensure his cabinet has gender parity, to reflect Labor's ranks.
The Liberal and National parties met on Monday and elected new leaders.
Former defence minister Peter Dutton became leader unopposed, with former environment minister Sussan Ley his deputy.
Nationals deputy David Littleproud replaced Barnaby Joyce as leader, with senator Perin Davey his deputy.
Mr Albanese's new frontbench will be sworn into office on Wednesday.
