The IEA forecast that non-OPEC supply - which includes the US - was set to rise by 600,000 barrels a day in 2017, and 1.6 million barrels a day in 2018.
An OPEC delegate suggested that it is likely the producers will agree on a period of 9 months for the extended production cuts.
Brent crude futures were up 47 cents, or 0.8 percent, at $62.91 a barrel at 11:49 a.m. (1649 GMT).
The forecast for 2018 for non-OPEC supply is "associated with significant uncertainties", particularly with regard to developments in U.S. shale oil. Stocks fell by 5.1 million barrels in the week to December 8, the fourth consecutive week of decline, to 442.99 million barrels, the lowest since October 2015.
An analyst at Taipei, Taiwan based Clifford Beaumont stated that the OPEC (Organization of the Petroleum Exporting Countries) group and its allies hope to end a worldwide supply glut of crude oil by extending the production cuts and thereby avoiding another price crash. Prices were 0.1% lower for the week.
An oversupplied market for crude oil, led by gains from USA shale oil and a previous OPEC policy of defending its market share with robust production levels, pushed oil prices below $30 per barrel in early 2016.
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Opec and 10 of its partners, including Russian Federation, agreed in November to extend a 1.8-million bpd supply cut throughout the whole of 2018 to force a drawdown in global inventories and support crude prices.
The IEA estimates that the average call on Opec crude in 2018 will be 32.5 million bpd, around 100,000 bpd higher than the average so far this year of around 32.4 million bpd, implying an ongoing drawdown in inventories.
The agency's current outlook for 2018 "may not necessarily be a happy New Year for those who would like to see a tighter market", as total growth in supply could exceed demand growth, which is now expected at 1.3 million bpd for 2018.
The agency has raised its forecast for total United States crude oil to 390,000 barrels a day for this year and 870,000 barrels a day for 2018, resulting in a worldwide surplus of 200,000 barrels a day in the first half of 2018, before reversing later in the year.
Nevertheless, looking at the year as a whole, there could be "a closely balanced market", the IEA added.