Polling stations opened at 8 a.m. local time (2200 GMT) and will close at 6 p.m.
Some 17.2 million voters choose the 151 seats in the House of Representatives for a three-year term. Forty of the 76 Senate seats are also renewed for six years. The party or coalition that wins the majority in the lower house will automatically be responsible for forming the government.
Opposition Labor leader Anthony Albanese, a slight favorite in the polls to become the next prime minister, has asked voters to “give him a chance”.
“Give this country a chance, we have plans,” said Mr Albanese, who described current Conservative Prime Minister Scott Morrison as “the most divisive I have ever seen”.
Mr Morrison, in power since 2018 and seeking re-election, appears to have reduced Labor’s lead in the polls in recent days, although he still appears to be trailing.
He accused his rival of showing “excessive pride” by claiming to be already sure of winning.
The last two polls published before the election, Thursday and Friday, gave Labor a six-point lead, but the gap was tending to narrow.
Both sides are trying to woo voters who are worried about the rising cost of living, with annual inflation at 5.1% and wages not keeping up in real terms.
– Climate issue –
In a country marred by increasingly severe floods, fires and droughts, Labor promises to do more for the environment.
Mr Morrison backs the coal and gas industries, and has resisted global calls for carbon cuts beyond the current pledge of -28% by 2030.
Voting is compulsory in Australia, and abstainers face a fine of 20 Australian dollars (13 euros).
Election officials changed the rules at the last minute to allow more Covid-19 positive people to vote by phone, in this first federal ballot since the start of the pandemic.
Scott Morrison hammers home the message that worked last time: Labor cannot be trusted when it comes to the economy.
He boasted of new data showing Australia’s unemployment rate fell to 3.9% in April, its lowest level in 48 years, as an “extraordinary achievement” that shows his plan is working.
He called Mr Albanese a “fragile element” because of his high-profile gaffes, including his forgetting about the national unemployment rate in front of the press.
“That’s the kind of stuff prime ministers need to know,” Mr Morrison said in an interview on Friday. “We have seen that he is not up to the task and that it is beyond him”.
Mr Albanese meanwhile promised firm action against corruption, after the failure of the Morrison government to set up a federal anti-corruption policeman.
He called the Morrison administration “the least open and least fair junk government in Australian political history”.
Anthony Albanese, 57, is a working man, brought up in Sydney council housing by a single mother. Of Italian origin through his father, he would be, if elected, the first Australian head of government not to bear an Anglo-Saxon or Celtic name.
But his opponent Scott Morrison, 54, is tough. Three years ago he won re-election despite unfavorable polls in what he called a “miracle”.