In its annual Medium Term Oil Market report the IEA said that the oil market has changed "dramatically" since last year's report.
The stock building of the past three years has been the highest since 1994-1999, and prices have fallen to levels last seen in 2003.
"Our analysis of the oil market fundamentals at the start of 2016 is clear that in the short term there is unlikely to be a significant increase in prices," Fatih Birol, executive director of the IEA said in his foreword to the report.
However, although the low price of oil has seen many projects postponed in 2015/16, these will come back into play as soon as prices recover, the IEA predicted.
"The price of oil will not need to recover to the $100 per barrel level we saw from early in 2011 to mid-2014 to allow this to happen," Birol said.
When oil prices do rise, they are likely to do so slowly, Birol said, as the availability of new supply "will put a cap on how far and how fast they can go".
Global oil production will rise by a total of 4.1million barrels per day (bpd) between 2015 and 2021, down from the 11m bpd between 2009 and 2015, as low oil prices discourage exploration and production capital expenditure.
The IEA expects US output of 14.2 mbd by 2021, as operational efficiencies and cost cutting allow production to grow again. This would make the US the largest contributor to supply growth over the next five years.
"Anybody who believes that we have seen the last of rising LTO [light tight oil] production in the United States should think again," said the IEA.
After a decline of 600,000 bpd in 2016, non-OPEC supply will recover from 2018. By 2021, non-OPEC output will reach 59.7m bpd, 2m bpd higher than last year’s levels, the report said.
Iran is likely to like supply growth in the OPEC producers, but this will depend on any re-imposition on sanctions, the IEA said.
" Looking further ahead, Iran will also strive to reclaim its spot as OPEC’s second biggest crude oil producer after Saudi Arabia – a post now occupied by Iraq. But with Iraq now pumping more than 4m bpd, Tehran will have its work cut out. Indeed, Iraq is expected to maintain its lead through the forecast period," the IEA said.
In January the IEA warned that the world could "drown in oversupply" as Iran's oil came on-stream.
The market could see a third successive year when supply will exceed demand by 1 million bpd and there will be "enormous strain on the ability of the oil system to absorb it efficiently", it said.
In a recent report, the Saudi Arabian National Commercial Bank (NCB) said that oil oversupply will continue and will keep oil prices at an average of $50 a barrel in 2016. OPEC members have continued to produce over the 30m bpd quota for the 18th month in a row, it said.