Prime Minister Malcolm Turnbull has described the latest labour force figures in which unemployment sank to a 2018 low of 5.4 per cent as "another great day for jobs".
A further 12,000 Australians found work in May, building on a revised 18,400 increase in April when the one million-mark was crossed for new jobs secured since the coalition came to power in September 2013.
"Jobs and growth is what we said in 2016 and we are delivering on it," Mr Turnbull told reporters in Cooee, Tasmania on Thursday.
"We have got the policies that are building a stronger economy."
Finance Minister Mathias Cormann said the next instalment of the government's plan will come before the Senate over the next parliamentary sitting fortnight when senators can vote for personal income tax relief and back a globally competitive company tax rate.
Both the remainder of the government's 10-year business tax plan and the multi-phased, seven-year personal income tax package are due to be voted on in the upper house, which sits from Monday.
"To keep our business taxes in Australia high when countries around the world are lowering theirs helps business overseas take jobs and investment away from Australia," Senator Cormann told reporters in Sydney.
"Clearly that is not the right way forward."
While fewer Australians found employment than had been expected by economists, the drop in the unemployment rate from 5.6 per cent in April was a surprise and partly reflected a fall in the number of people looking for work.
The employment rise reflected a 32,600 jump in part-time workers that was partly offset by a 20,600 drop in full-time staff.
Labor's employment spokesman Brendan O'Connor jumped on this employment mix, saying it is a story of growing under-employment.
The latest figures showed the under-employment rate - those in work but seeking extra hours - rose to 8.5 per cent or 1.1 million people.
"We have too many workers not being able to find sufficient work ... you have people struggling to get sufficient means to make ends meet, to pay for the bills, to put food on the table, to pay for school fees," Mr O'Connor told reporters in Brisbane.
The result does not change the interest rate outlook.
"Interest rates will remain on hold until there is firm evidence that skill shortages are leading to broader-based increases in wages," Commonwealth Securities chief economist Craig James said.
It means the Reserve Bank won't be about to join the US Federal Reserve, which lifted its key rate for the seventh time in the past few years on Wednesday.
It now puts the US Fed funds rate at a 1.75-2.0 per cent range compared to the Australian cash rate at a record low 1.5 per cent, where it has stood since August 2016.