The fall in unemployment has been welcomed, but some analysts warn that the UK's jobs recovery is reaching its limits.
Josh Hardie, deputy director general of the CBI, said: "While it's encouraging that employment has risen there are some signs of a softening in the labour market, particularly with job vacancies falling back.
"However, continued uncertainty could be weighing on hiring intentions. In addition we are seeing evidence that employers are considering the impact of the National Living Wage, introduced last month."
TUC general secretary Frances O'Grady said: "While the employment rate has recovered, it seems to be at the cost of decent pay growth and the quality of jobs.
"Seven years on from the financial crisis, we should be in a much better place, but with the economy slowing down there is a danger that the lost ground on wages will never be recovered."
David Kern, chief economist at the British Chambers of Commerce, said: "Although the UK employment rate reached a record high, the cumulative picture - including manufacturing, trade and GDP figures - points to a softening in economic activity."
Mike Cherry, chairman of the Federation of Small Businesses, said: "The unemployment rate remains at a historically low level, but there are warning signs that the economy is not performing as well as many had hoped.
"Our members' confidence remains comparatively low, with businesses looking to contain costs amid a challenging policy environment."
Alun Cairns, Secretary of State for Wales, said: "This is a hat-trick of good news for the Welsh jobs market. Across the country, the investment we have put into rebalancing the economy and welfare reform is now paying dividends with record numbers coming off benefits and into work.
"Yet again, we are seeing an unemployment rate below the national average as Wales shows an increasingly confident and entrepreneurial face to the world."
Owen Smith, shadow work and pensions secretary, said: "It is welcome that unemployment has fallen slightly, after a sharp rise in the last set of figures. However, people continue to struggle through a Tory decade of record low pay, which is resulting in earnings growth remaining far too slow."
Laura Gardiner, of the Resolution Foundation, said: "Despite record-high employment, there are clear signs that the remarkable post-crisis pace of labour market recovery has been slowing in recent months.
"While uncertainty associated with the EU referendum may well have contributed a little to this cooling, the truth is that employment has been broadly flat since October last year.
"Given this backdrop, today's figures instead suggest that the UK's jobs recovery is reaching its limits."
Jim Hillage, director of research at the Institute for Employment Studies, said the figures gave m ore evidence that the labour market was starting to "plateau".