At last count, U.S. crude stocks stood at a record 468 million barrels, the IEA said.
"U.S. stocks may soon test storage capacity limits. That would inevitably lead to renewed price weakness, which in turn could trigger the supply cuts that have so far remained elusive," the IEA said.
"While the U.S. supply response to lower prices might take longer to kick in than expected, it might also prove more abrupt," it said, adding that growth would abate in the second half of 2015.
The IEA's conclusions will disappoint OPEC, which kept its output steady at the group's last meeting in November to protect market share and stifle U.S. oil output growth.
In the second quarter of 2015, when demand is at its weakest due to global refinery maintenance, the need for OPEC crude will be 28.5 million bpd, the IEA said - compared to the group's current output of 30.22 million bpd in February.
Tentative signs of recovery
The IEA raised its demand forecast for the second half of 2015, which in turn led to a higher call on OPEC crude of 30.3 million bpd in the same period—closer to the group's real production levels and the official target of 30 million bpd.
Having bottomed in the second quarter of 2014, global oil demand growth has since steadily risen, with year-on-year gains estimated at 1.0 million bpd for the first quarter of 2015, the IEA said.
The forecast of demand growth for 2015 as a whole has been raised by 75,000 bpd to 1.0 million bpd versus the last report and versus the 680,000 bpd growth seen in 2014, bringing global demand this year to an average of 93.5 million bpd.
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"Tentative signs of a demand recovery have emerged with the turn of the year, with a heavy emphasis reserved for the word 'tentative'," the IEA said.
In other bullish factors—beyond political instability in certain producing countries such as Iraq and Libya—refined product markets have proved unexpectedly strong, the IEA said.
"Not only have product prices lagged those of crude during the selloff—as is common in a downturn—but they have raced ahead of them in the rebound, keeping refining margins remarkably firm, and supporting unexpectedly strong throughputs in once-depressed refining centers such as Europe and OECD Asia," the IEA said.
"Product demand has shown signs of life, with even European demand emerging from a secular decline to show strong growth of 3.2 percent in December and 0.9 percent in January."