Next year, demand is seen hitting 98.9 million bpd, up 1.3 million bpd from this year.
Unless OPEC agrees to cut more production, output from non-member states will leave the market in surplus and limit the rally in oil prices, the IEA said.
Reducing the use of fossil fuels is a key demand from activists and many governments taking part in the global climate talks in Bonn, Germany, this week.
"Even after some modest reductions to growth, non-OPEC production will follow this year's 700,000-bpd growth with 1.4 million bpd of additional production in 2018 and next year's demand growth will struggle to match this", the IEA said.
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In Abu Dhabi on Monday, the UAE Minister of Energy and Industry Suhail bin Mohammed Faraj Faris Al Mazrouei, said that oil producers were expected to unanimously extend a production cut accord later this month, but its duration was still under discussion.
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After an upbeat performance last week, oil prices edged lower for a second day Tuesday.
The largest disruptive force to supply will be shale production in the U.S. - the IEA estimates USA crude oil will reach peak output in the 2020s of around 17m bpd.
The IEA also revised down its 2018 oil demand forecast for Brazil from 3.15 million bpd to 3.13 million bpd.
While the IEA's base-case scenario projects oil prices reaching US$83 per barrel by 2025 and as high as US$111 by 2040, a low oil-price scenario could see prices stuck in the US$50 to US$70s if electric passenger cars take off, USA tight oil production continues to rise and upstream costs decline.
Chris Watling, CEO and chief market strategist at Longview Economics, was quoted as saying that the adoption of EVs could lead to global peak oil demand as soon as 2023, which will result in oil prices crashing to $10.
In addition, analysts said oil prices were pressured by a global commodities selloff, led by base metals like nickel and copper, due to weaker-than-expected economic data from China.
"None of its core scenarios for the future of energy provide a reasonable chance that the world will avoid climate catastrophe", said Adam Scott, senior advisor at Oil Change International.