Brent for June settlement climbed 3 cents to $US55.89 a barrel on the London-based ICE Futures Europe exchange.
"It can be argued confidently that the market is already very close to balance, and as more data becomes available this will become clearer", it said in the report.
But the organisation predicted supply would grow in coming months, with USA oil-producing firms driving the increase. They have averaged about $55 a barrel so far this year, up from about $45 a barrel for the whole of last year, as the production restraint deal by Opec and 11 non-Opec producers has begun to eat into the record world oil stockpile.
Still, the IEA said, global oil supply and demand appear to be rebalancing after more than two years of oversupply.
Indeed, although the oil market will likely tighten throughout the year, overall non-OPEC production, not just in the United States, will soon be on the rise again.
Then in December, non-OPEC producers led by Russian Federation agreed to cut their own output to 558,000 barrels per day.
"It is now half time for the six-month oil production cuts agreed by Opec and eleven non-Opec countries".
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"We have an interesting second half to come", it said.
"This would provide further support to prices, which in turn would offer further encouragement to the USA shale oil sector and other producers", the IEA added.
As with Wednesday's report from Opec in Vienna, the IEA sees the USA as the main contributor to net growth this year of almost 500,000 bpd after a dip last year of almost 800,000 bpd, with the U.S. expected to raise production by 680,000 bpd.
That is less than the organisation had anticipated previously and could prove an "optimistic" forecast, it said.
"The net result is that global stocks might have marginally increased in the first quarter versus an implied draw of about 0.2 million bpd", the IEA said.
Non-OPEC producers such as Azerbaijan, Bahrain, Brunei, Equatorial Guinea, Kazakhstan, Malaysia, Mexico, Oman, Russia, Sudan, and South Sudan agreed to reduce output by 558,000 barrels per day starting from January 1, 2017 for six months, extendable for another six months.
The combination of factors could keep a lid on oil prices, which have risen in the past six months after a three-year slump.