Labor starts with 68 seats, plus notionally the new Victorian seat of Hawke, and required 76 seats for a majority in the 151-seat House of Representatives.
Scott Morrison's government went into the election holding 75 seats, having lost Stirling in WA in a redistribution.
Seven lower house crossbenchers are hoping to hold their seats and 40 are up for grabs in the half-Senate election.
Labor leader Anthony Albanese has pledged to "unite the country" if he becomes Australia's 31st prime minister.
Mr Albanese cast his vote in his Sydney seat of Grayndler, and said Labor was kicking with the wind at its back.
"I want to represent all Australians. I want to unite the country," he said.
"I'm positive and hopeful about a good outcome."
The Labor leader says people want a change of government, as well as action on climate change, secure work and the reinvigoration of local manufacturing.
The prime minister is promising "different gears" to his self-described bulldozer approach if re-elected, but says tough tactics were needed as he steered Australia through the COVID-19 pandemic.
He warned voters against supporting independent candidates which increased the chances of a hung parliament.
"What Australia needs is someone who knows how to manage money, knows how to deal with our national security interests, knows how to be able to move forward," he said.
Mr Morrison also revealed an asylum seeker vessel on its way to Australia was turned back last week, and seized on the news to spruik his government's tough border policies.
Former Liberal minister Christopher Pyne predicted a Labor win, expecting the party will gain seats numbering in the "high 70s".
"If we win today, it will be very surprising," Mr Pyne told the Seven Network.
"Labor will win but, I think things very much tightened up in the last six weeks and what looked like a blowout … is obviously much closer."
Mr Pyne said he didn't expect a result on Saturday night, and that the coalition would win seats numbering in the mid-60s, with up to seven independents elected.
Another former minister, Julie Bishop, told Nine: "If Scott Morrison is able to pull off a second miracle, it really will be an extraordinary outcome. ... I don't understate incumbency. It's a powerful advantage. But I think tonight, we're going to see some very interesting head-to-head contests."
Greens leader Adam Bandt cast his vote in his seat of Melbourne, with his party hoping to boost its presence in the Senate and the lower house.
If the Greens find themselves in a balance of power situation they will push for dental and mental health being covered by Medicare, more affordable homes, free child care and more ambitious action on climate change.
The latest Newspoll in The Australian showed Labor 53-47 despite a two point drop in its primary vote to 36 per cent.
If reflected in the poll count on Saturday, this would deliver Labor 83 seats to the coalition's 61 with seven crossbenchers.
The election will be won and lost in about 25 marginal seats across NSW, Tasmania, Victoria, WA, SA and Queensland.
Two out of the past four elections have not seen a clear result on election night, with the electoral commission confirming 2.7 million postal vote applications had been received.
Both major party leaders will be attending functions in Sydney on Saturday night.
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