The unemployment rate for men was unchanged at 4.5 percent while for women it went down by 0.1 percent to 3.9 percent.
There were 1.81 million jobless people, down 0.5 percent from the previous month while employment was steady at 40.81 million.
Compared with a year earlier, the number of unemployed persons declined 8.1 percent and employment rose 2.2 percent.
Youth unemployment rate came in at 7.2 percent, lower than 7.3 percent in April, but slightly higher than 7.1 percent a year earlier.
Separate data from the Labour Office showed the number of unemployed persons fell by 6 thousand to 2.69 million in June from May of 2016. The unemployment rate was unchanged at 6.1 percent.