The regional jobless tally is 174,000 or 6,5% - 3,000 fewer than the previous quarter.
But nationally the total went up by 25,000 in the quarter to June, the first time there have been two consecutive rises for two years.
The Office for National Statistics (ONS) said it was possible the jobs market was “levelling off”.
Other figures showed that the number of people claiming jobseeker’s allowance fell by 4,900 last month to 792,400 following a slight increase in June.
There were 31 million people in work in the latest quarter, 63,000 fewer than the three months to March, but 354,000 more than a year ago.
A record 14.5 million women are in work, while employment for men slumped by 71,000 to just under 16.5 million compared with the previous quarter.
ONS statistician David Freeman said: “This is now the second consecutive time we’ve reported fewer people in work on the quarter.
“While it’s too early to conclude that the jobs market is levelling off, these figures certainly strengthen that possibility. Growth in pay, however, remains solid.”
Average earnings increased by 2.4% in the year to June, down by 0.8% on the previous month, but still ahead of inflation.
The number of people classed as economically inactive, including those on long-term sick leave or who have given up looking for work, has increased by 7,000 to just under nine million.
The number of UK nationals in work between April and June increased by 84,000 compared with a year ago to 27.7 million. The total for non-UK nationals increased by 257,000 to 3.1 million.
Work and Pensions Secretary Iain Duncan Smith said: “Thanks to our long term economic plan we have already seen two million more people in jobs since 2010. On top of that, today’s figures show job vacancies at a near record high - evidence of the continued confidence of British businesses, and potential for further growth in the UK economy.
“Our one nation government is helping millions across the country to succeed and achieve their full potential. I was particularly pleased to see that wages are continuing to rise - meaning that hardworking people will see a real difference in their pay packets.”
The Government pointed out there were nearly two million more people in work than in 2010, with almost half a million more jobs in the private sector over the last year.
Unemployment has fallen by 221,000 in the last year, and long-term unemployment has been cut by more than 210,000 since 2010
There are job 735,000 vacancies, an increase of nearly 70,000 since last year. The claimant count has fallen by more than by more than 200,000 in the last year.
Wales’s First Minister Carwyn Jones said: “Today’s figures show employment in Wales at a record level as we have outperformed every other part of the UK.
“Over the past quarter we have seen 42,000 more people in employment in Wales, compared to falling employment for the UK over that same time.
“Unemployment in Wales has also fallen by 9,000, in contrast with increasing unemployment across the UK.
“Over the last year Wales has also outperformed every other part of the UK to record the highest increase in employment rate and the largest decrease in claimant count.”
Stephen Timms, acting shadow work and pensions secretary, said: “The rise in unemployment for a second month in a row is worrying and shows we cannot afford to be complacent about the recovery.
“With productivity stagnating, David Cameron and George Osborne must take bolder action to raise jobseekers’ skill levels to get more back into work and help build the high-skilled workforce Britain needs.
“The rise in youth unemployment highlights a real danger that young people are being left behind. Ministers must urgently deliver more high-quality apprenticeships to give young people the skills they need to get a job and build a future.”
Matthew Whittaker, chief economist at the Resolution Foundation, said: “Britain’s pay recovery looks set to continue throughout 2015, helped along by historically low inflation. But with average earnings having only recovered up to their August 2004 level, there is still a huge amount of ground to make up.
“We’re seeing some significant differences in pay growth across the sectors. Most obviously, private sector pay is rising much more rapidly than public, but it’s encouraging to see growth of 4% in the low-paying retail sector. However, manufacturing pay growth stands at just 1.3%, well short of the 4.3% recorded in the finance sector.
“It’s a concern that the employment recovery isn’t doing more to boost the pace at which people move jobs. This needs to increase before we can expect to see strong real wage growth over the medium term.
“After two years of remarkable jobs growth the UK employment rate is starting to level out. It’s likely that we’re nearing the limits of what’s possible through employment ‘catch-up’ alone.
“Moving further - and heading towards full-employment - is likely to require a new bout of concerted policy action designed to support employment among those groups who are traditionally further away from the labour market.”
Chris Jones, chief executive of the City & Guilds Group, said: “The steady stream of good news has now run dry as unemployment has risen for the second consecutive quarter. With many predicting last quarter’s rise to be a blip, it’s concerning that a trend is developing.
“But 16% of young people are still unemployed. Clearly we need to do a lot more to help set young people on the path to success.”