* Unemployment rate - 4.9 per cent versus 5.1 per cent in May

* Underemployment rate (employed people seeking additional work) - 7.9 per cent versus 7.4 per cent

* Employment rose 29,100

* Full-time positions rose 51,600

* Part-time employment fell 22,500

* Participation rate (people working or looking for work): Unchanged at 66.2 per cent

STATE UNEMPLOYMENT RATES:

NSW - 5.1 per cent in June versus 5.1 per cent in May

VIC - 4.4 per cent versus 4.7 per cent

QLD - 5.1 per cent versus 5.4 per cent

SA - 5.3 per cent versus 5.8 per cent

WA - 5.1 per cent versus 4.6 per cent

TAS - 4.5 per cent versus 5.7 per cent

NT - 4.8 per cent versus 4.5 per cent

ACT - 4.9 per cent versus 3.6 per cent

(Source: Australian Bureau of Statistics)

Australian Associated Press