However, the unemployment rate of 7.8% is still above the 7% target rate set recently by the new Bank of England governor Mark Carney.
There are 29.78 million people aged 16 and over in employment. This is up 69,000 from January to March 2013, and up 301,000 from a year earlier.
The ONS figures showed average weekly earnings excluding bonus payments rose by 1.1% when comparing April to June 2013 with the same period 2012.
Average weekly earning including bonuses rose by 2.1% when comparing the same periods. This is the first time the growth rate has exceeded 2% since December 2011.
Recruitment and Employment Confederation CEO Kevin Green said the figures prove UK is heading in the right direction.
"The UK labour market has performed incredibly well over the last few years, meaning we are not experiencing the devastating levels of mass unemployment seen elsewhere in Europe," said Green.
"The concern for people who have been out of work for over a year is that even when new jobs become available they often won't have the skills, experience or confidence to take advantage of those opportunities."