Early data for August is also gloomy with the number of employees in the United Kingdom on payrolls down by about 695,000 from March compared to 659,000 in July, according to the ONS.
Compared with the same time a year ago there were 2,000 fewer jobs.
Business Minister Jamie Hepburn said: "For the period May to July 2020, Scotland's employment rate estimate rose slightly over the quarter to 74.3% and the unemployment rate estimate also rose slightly over the quarter to 4.6%". The claimant count rate came in at 7.6% vs. 7.5% last.
In June, 316,500 employees in Wales were paid 80% of their salaries under the United Kingdom government's furlough scheme, figures from the Treasury showed.
The Office for National Statistics (ONS) showed on Tuesday, the UK's official jobless rate ticked higher to 4.1% in July vs. the previous 3.9%, while the claimant count change showed a smaller-than-expected increase last month.
"That means building on the furlough scheme by setting up a new job retention and upskilling deal, to keep people employed at firms that have a viable future", she said.
Matthew Percival, Confederation of British Industry director of people and skills, said: "The easing of lockdown restrictions and a more flexible Job Retention Scheme in July have led to the beginning of a recovery in vacancies and hours worked".
Analysts worry that unemployment will start to rise more markedly in coming months as the package, which was used by more than a million companies to keep almost 10 million employees on payroll, ends on October 31.
That is while 400,000 employees in Wales have been off work on furlough.
Comparing the figures up to July with those up to April in Wales, unemployment went up 1,000.
Another way of looking at what's happening in workplaces is to see how many people are on employer payrolls and that is down 695,000 across the United Kingdom since coronavirus hit in March.
It is a relief that unemployment has increased at a slower rate in Wales than the United Kingdom as a whole. That could now be happening with unemployment.