UK unemployment fell 26,000 in the three months to May to 2.45 million, official figures show.
The unemployment rate was 7.7%, according to the Office for National Statistics (ONS), down from 7.8% in the previous quarter.
However, the number of people claiming Jobseeker's Allowance in June rose by 24,500 to 1.52 million - the biggest such increase in two years.
It follows an upwardly-revised 22,500 rise in the claimant count for May.
The total number claiming unemployment benefits reached its highest level since March 2010, while the claimant count rate held steady at 4.7%.
It is the second month in a row that the claimant count has risen while the unemployment total - which is based on separate data - has fallen.
The ONS said it was not unusual for the two figures to move in opposite directions as they measure different things and cover different time periods.
The employment report said that the number of long-term unemployed fell by 37,000, although there was also an 11,000 increase in the number of people out of work for less than a year.
The number of 16 to 24-year-olds out of work fell by 42,000.
Many economists look at the claimant count as a more current indicator of the health of the labour market.
"While [the unemployment survey] data suggest some tentative improvement... more up-to-date information suggests that weakness lies ahead," said Chris Williamson, economist at research firm Markit.
"The number of job vacancies... fell by 7,000 between the first and second quarters of the year, and Markit's recent survey of recruitment consultancies showed that the number of people placed in permanent jobs showed the weakest rise for 22 months in June."
The total number in employment rose 50,000 versus the previous quarter to 29.28 million - the highest total in more than two years.
Pay also continued to rise at a subdued rate.
Average earnings, excluding bonuses, rose a faster-than-expected 2.1% in the three months to May - well short of the inflation rate, which fell slightly to 4.2% in June.
"It's worth remembering that employment didn't fall nearly as much as expected in the recession, partly because businesses retained staff through short-time working, wage cuts and other mechanisms," said Nigel Meager, director of the Institute for Employment Studies.
"The other side of this coin, however, is that many employers now have the staffing capacity to respond when the economy returns to growth, without hiring new people.
"Given that growth itself is fairly weak, it's unsurprising that the overall labour market remains in an anaemic state, as confirmed by these figures."
The employment report indicated that the number of new jobs created in the private sector was still outstripping government job losses.
The public sector workforce shed 24,000 during the three months to May, far less than the 104,000 new positions created by the private sector.
"Today's headline unemployment figures show some encouraging news," said TUC general secretary Brendan Barber.
"However, looking at the data more closely, there are worrying signs for the future."
Besides the rise in the claimant count, he also pointed to "a big jump in the ratio of unemployed people to job vacancies, from a national average of five people chasing each job to 5.4".
"There are parts of London and Scotland where around 30 dole claimants are chasing every vacancy - and in Haringey there are 39 people after every available job."
David Kern, chief economist for the British Chambers of Commerce, agreed that there were causes for concern among the generally positive figures.
These included a rise in the number of economically inactive people, and a new record number of people working part-time because they could not find a full-time job.
"The private sector is willing and able to create jobs, but we must not be complacent," he said.
"It is likely we will see more public sector job cuts in the coming months, and we are expecting unemployment to increase by 150,000 to a peak of 2.6 million over the next 12 to 15 months."