While Russia's willingness to stick to the deal throughout 2018 has been questioned, on Monday OPEC's Secretary General Mohammed Barkindo assured U.S. cable channel CNBC that Russian President Vladimir Putin had promised Russia would keep the bargain.
The oil cartel and key ally Russian Federation have spent more than a year trying to drain the world of excess supply.
The IEA's "Oil Market Report", issued every month, said new and revised data show a "modest" tightening early this year in the worldwide oil balance. It could soon challenge Russian Federation for the global crown.
On Monday, OPEC announced its expectation that global demand would increase by 1.59 bpd in 2018, to 98.6 million bpd.
The International Energy Agency, a policy adviser to countries, says in its monthly report that "in 2018, fast rising production in non-OPEC countries, led by the US, is likely to grow by more than demand".
"Another sobering thought is that it is not just a matter of production: trade patterns are changing", they said.
USA shale production is growing faster in 2018 than it did even during the boom years of $100 a barrel oil prices from 2011 to 2014, said the International Energy Agency in its closely watched monthly report.
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OECD stocks now stand at 52m bbl in excess of the historic average, compared to 264m above a year ago, the Paris-based agency said.
However, the higher prices will also encourage non-member producers, such as the USA, to pump more oil, contributing to a worldwide glut. But many emerged leaner and stronger than before.
The producers agreed in November to extend self-imposed limits on output until the end of this year, seeking to counter a glut fed partly by USA shale drillers. This would shift the expiration date of the agreement from March to the end of 2018.
But there are signs that the strategy may be losing its effectiveness.
The steady decline of the USA dollar has helped drive up crude prices for weeks, but that came to an abrupt halt last week.
Brent for April settlement rose 42 cents to $63.01 a barrel on the London-based ICE Futures Europe exchange.
The IEA said oil prices, which briefly touched a high of $71 a barrel in January, could be supported even if U.S. production rises, provided global growth remains strong, or if unplanned supply outages persist. "If so, most producers will be happy, but if not, history might be repeating itself".