The unemployment rate is set to head lower in coming months with job advertising remaining strong in May.
The latest ANZ job ads report is consistent with jobless rate of five per cent compared with the 5.5 per cent rate as of April.
Job ads increased by 7.9 per cent in May - the 12th straight month of gains - to be 38.8 per cent up on pre-pandemic levels.
"With the unemployment rate having fallen for six consecutive months and more people in work than before the pandemic our economic plan is working," Treasurer Josh Frydenberg said.
Mr Frydenberg was responding to global rating agency Standard & Poor's decision to lift Australia's credit rating outlook to stable from negative, indicating the nation's top-tier AAA rating is safe.
"Australia remains one of just nine countries to hold a AAA credit rating from the three major rating agencies," the treasurer said, pointing to the outlook lift as a sign of confidence in the Morrison government's management.
Being on a negative outlook meant Australia was at risk of losing its AAA status in the next two years, potentially raising the cost of borrowing for government, big business and banks in overseas markets, which in turn could be passed on to consumers.
ANZ economists have recently upgraded their employment forecasts and now expects the jobless rate to be 4.8 per cent by the end of this year and 4.4 per cent by end-2022.
"We think solid employment growth will drive this rapid improvement, notwithstanding near-term volatility post-JobKeeper," ANZ senior economist Catherine Birch said.
Such strong demand for workers backs Treasury secretary Steven Kennedy's hope that people who have lost their jobs as a result of the JobKeeper wage subsidy ending will quickly find employment in coming weeks.
Addressing a Senate hearing last week, Dr Kennedy estimated that about 56,000 people lost jobs in the four weeks following the JobKeeper scheme ending in March.
In March, he had predicted up to 150,000 people could lose their jobs.
Meanwhile, Australia's services industry is growing at its fastest pace in almost 18 years as the sector extends its recovery from the doldrums of last year's coronavirus-induced recession.
The Australian Industry Group performance of services index rose by 0.2 points to 61.2 in May, its highest monthly result since October 2003.
Ai Group chief executive Innes Willox said there was particular strength in logistics, business and property, and retail trade and hospitality services.
"Across the services sector, sales and employment grew impressively and input costs, wages and selling prices continue to rise at a steady clip," Mr Willox said.
The data was complied before the latest COVID-19 lockdown in Victoria.
"Although new orders for services grew strongly in May, close attention will now be on the impacts of the latest cluster of cases and the Victorian lockdown on business sentiment in the weeks ahead," Mr Willox said.
But Ms Birch does not expect the lockdown that is due to end on Thursday to derail the state's labour market recovery.
"Even if we see some employment losses in June, as long as restrictions start easing from June 11 as currently planned, workers should be reinstated or find new jobs quite quickly, given the underlying strength in the labour market," Ms Birch said.