UK unemployment fell by 57,000 to 2.51 million in the three months to May, the Office for National Statistics said.
Youth unemployment fell by 20,000, but the number of long-term jobless hit a 17-year high.
The number of Jobseeker’s Allowance claimants in June fell by 21,200 to 1.48 million, the first fall below 1.5 million for nearly three years.
Ministers said it showed that recovery was taking hold, but critics said the human costs were still too high.
Separately, the ONS reported that average earnings increased by 1.7% in the year to May, up by 0.2% on the previous month, giving an average weekly wage of £476.
The unemployment rate was 7.8%, the ONS data showed. The number of people in employment rose by 16,000 to a total of 29.7 million.
However, 915,000 people have been out of work for more than a year, the ONS figures showed, an increase of 32,000 and the highest total since 1996.