The leader of the Liberal-National coalition needs to win 76 out of 150 lower house seats to form a ruling majority.
With about half the votes counted, results suggest a very close contest.
Opposition Leader Bill Shorten said the close result was a vindication of his Labor party’s policies.
Labor has improved strongly on its 2013 election result of 55 lower house seats.
“There is one thing for sure – the Labor Party is back,” he said.
All 150 seats in Australia’s lower house, the House of Representatives, are up for grabs at the election, as are 76 seats in Australia’s upper house, the Senate.
It is the first time in decades that all the seats in both houses have been up for election.
The double-dissolution election, as it is known, was called by Mr Turnbull in an attempt to break a deadlock over industrial relations legislation.
It was thought the result of the UK’s referendum on the EU would benefit Mr Turnbull, who assured voters that he could deliver “economic certainty”.
The former lawyer and investment banker vowed to deliver tax cuts for workers and small businesses.
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Source: BBC