The number of unemployed in Scotland increased by 3,000, to stand at 107,000. UK unemployment fell by 57,000 over the same period.
However, Scotland's jobless rate of 3.9% was below the UK figure of 4.4%.
The number of people in work in Scotland reached 2.65m, according to the Office for National Statistics (ONS).
Meanwhile, wage increases continued to fall further behind inflation.
Excluding bonuses, earnings rose by 2% year-on-year. However, inflation had hit an almost four-year high of 2.9% in May.
When the impact of inflation is factored in, real weekly wages fell by 0.5% compared with a year earlier.
Scottish unemployment rose slightly in the three months to June, while falling across the UK as a whole.