About 900 jobs were added for the month compared to the 33,500 in August, with the participation rate staying the same at 66.6 per cent.
"With employment increasing slightly, by around 1000 people, and the number of unemployed increasing by 9000, the unemployment rate rose by less than 0.1 percentage point but remained at 3.5 per cent in rounded terms," the bureau's Bjorn Jarvis explained.
In August, the Australian Bureau of Statistics' jobless rate rose slightly to 3.5 per cent from 3.4 per cent as more people started looking for work, with illnesses keeping many away from the job market during the height of winter.
The treasurer also suspects COVID-related absences are keeping the unemployment rate low because employers have bolstered their workforces to make up for workers off sick.
"One of the reasons we've had unemployment so low is because employers have had to try and build bigger workforces to make up for what has been a lot of absenteeism, COVID-related and otherwise," Jim Chalmers told ABC radio on Thursday.
The latest ABS labour force figures reveal a job market that's still competitive despite signs of cooling off in job ad and vacancy data.
The September Seek report showed a 5.2 per cent drop in job ad volumes, with small declines reported every month since May.
However, job ad volumes were still well above pre-pandemic levels.
Seek's managing director Kendra Banks said it was premature to call the end of the incredibly tight labour market.
Advertised salaries as measured by the job ad platform also eased slightly in August, suggesting the bidding war for talent was starting to ease.
Job vacancies as measured by the ABS also fell two per cent over the three months to August.
But businesses are clearly still struggling to find skilled workers, with labour shortages the top concern for business leaders, according to an Australian Institute of Company Directors survey from earlier in the week.
While the Reserve Bank of Australia welcomes record low employment, the central bank is conscious that a tight labour market puts pressure on wages and can fuel inflation.
In a speech last week, RBA deputy governor Michele Bullock said record low unemployment was starting to put upward pressure on wages.
She said this was one reason the central bank needed to lift interest rates further to bring inflation back within the two to three per cent target band and keep inflationary pressures anchored.
"Inflation is too high in Australia and is expected to rise further," she said.
"While a lot of this can be explained by global factors such as supply chain disruptions and energy prices, there is an important element of strong domestic demand."
Despite these concerns, at the October board meeting the central bank decided to slow down its rate hiking and lift by 25 basis points rather than 50 basis points.