Twelve out of 150 lower house seats remain in doubt, with counting of pre-poll, postal and absentee votes to resume on Tuesday.
The official Australian Electoral Commission tally has Labor on 67 seats and the ruling Liberal-National coalition on 66 seats.
Independents and minor parties gained an unprecedented share of the vote.
Analysts expect the remaining ballots to fall in favour of the government and Prime Minister Malcolm Turnbull said early on Sunday morning he expected to get the 76 seats he needs to form a new administration.
But many analysts are predicting a hung parliament, where neither party has an absolute majority.
In that case, both Mr Turnbull and Labor leader Bill Shorten will have the chance to form government by doing a deal with independents and minor parties.
Mr Shorten said in a speech that Mr Turnbull`s coalition had lost its mandate to govern.
Australia election: Tight vote could end in hung parliament
03 July 2016
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Australia will not know the result of its federal election for days as counting in tight seats continues.
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