However the Paris-based IEA cautioned that the recent sharp gains did not mean that the worst was over.
Around 1200 GMT, US benchmark West Texas Intermediate (WTI) for delivery in April added 90 cents to trade at USD 38.74 a barrel.
Brent North Sea crude for May delivery rose 73 cents to USD 40.78 a barrel compared with yesterday's close.
"A rebound in the oil price after the IEA called for a possible bottom has helped broader stock market sentiment," said CMC Markets analyst Jasper Lawler.
"The agency said oil demand remained constant and suggested falling high-cost supply and supply outages in Iraq have supported higher prices."
Oil had slumped from above USD 100 in mid-2014 to near 13-year lows in January earlier this year, before staging a modest recovery to current levels.
However, there is a long way to go before supply and demand find a real balance, probably in 2017, the IEA said Friday.
"International crude oil prices have recovered remarkably in recent weeks," the IEA noted in its monthly market report.
"This should not, however, be taken as a definitive sign that the worst is necessarily over. Even so, there are signs that prices might have bottomed out."
Among factors for higher prices are talks among producers launched by Saudi Arabia, Venezuela, Qatar and Russia to freeze production which the IEA said amounts to "a first stab at co-ordinated action that is intended to stabilise prices" with the presumed aim of pushing oil up to USD 50 a barrel.
The outcome of negotiations is, however, uncertain and a big supply overhang in the oil market means it would have little impact in the months ahead.
