Unemployment in the UK fell just 2,000 to 1.69 million in the first three months of 2016, according to the Office for National Statistics (ONS).
However, it contrasts with a 21,000 rise in unemployment between December and February.
The small decrease means the unemployment rate remains at 5.1%.
The ONS said, however, that there was a 44,000 rise in people in work. With 31.58 million people now in work, the employment rate reached an all-time high of 74.2%.
Average weekly pay rose 2%, including bonuses, and 2.1% excluding bonuses.
David Freeman, ONS statistician, said: “The employment rate has hit another record high, but this time the increase is quite modest. With unemployment very little changed, that is further evidence the jobs market could be cooling off.”
Michael Baxter, an economics blogger, said:" With employment at a record high and unemployment now quite modest, there is little scope for the UK to grow by increasing employment. Now the UK needs to focus on the three Ps - productivity, productivity and productivity. The gradual rise in the National Living Wage, controversial though it is, may force companies to focus on how they can raise productivity."