Employment rose by 60,600 in May

* Underemployment rate (employed people seeking additional work) - 5.7 per cent versus 6.1 per cent

* Employment - rose by 60,600

* Full-time positions - rose by 69,400

* Part-time employment - rose by 8700

* Participation rate (people working or looking for work) - 66.7 per cent versus 66.4 per cent in April

* Monthly hours worked in all jobs - rose by 0.9 per cent or 17 million hours

STATE UNEMPLOYMENT RATES:

NSW - 4.0 per cent in May versus 3.5 per cent in April

VIC - 3.7 per cent versus 4.2 per cent

QLD - 4.0 per cent versus 4.5 per cent

SA - 4.6 per cent versus 4.5 per cent

WA - 3.1 per cent versus 2.9 per cent

TAS - 4.5 per cent versus 3.8 per cent

NT - 4.1 per cent, unchanged from April

ACT - 3.3 per cent versus 3.1 per cent

(Source: Australian Bureau of Statistics)