On Tuesday, the U.S. Energy Information Administration said it expected the country's oil output to rise in February, with production from shale rising by 111,000 barrels per day (bpd) to 6.55 million bpd.
US West Texas Intermediate (WTI) crude futures CLc1 were at $63.63 a barrel, down 10 cents on the day and down from an earlier high of $63.96.
Both contracts climbed to their highest levels since December 2014 this week with Brent reaching $70.37 on Monday and WTI up to $64.89 on Tuesday.
Taken as a whole, however, total demand and non-OPEC production, namely USA shale, will grow more or less in parallel, and "that might act as the ceiling for aspirations of higher oil prices", the report read. Russian Federation does not plan to withdraw from the OPEC+ oil production limiting deal despite the current oil price above $70 per barrel, Energy Minister Alexander Novak told reporters on Tuesday.
Brent hit $70.37 on Monday, matching a high from December 2014, when markets were at the beginning of a three-year decline.
EIA in its Short Term Energy Report, released at the weekend, added that a brief pipeline outage in Libya, may have also affected waterborne crude oil supplies and contributed to the upward price pressure.
Money managers have raised the bullish positions in WTI and Brent crude futures and options to a record, according to data from the U.S. Commodity Futures Trading Commission and the Intercontinental Exchange. The cuts are set to last through 2018.
The price of crude oil is up more than 4 percent so far in the 11 global trading days of the year.More news: India, Australia tours are biggest challenges for England: Jos Buttler
The restraint has coincided with healthy oil demand, pushing up crude by nearly 15 per cent since early December. The market is tightening faster than expected because of "improving cyclical conditions", cold winter weather and strong OPEC compliance, the bank said.
Bank of America Merrill Lynch and Morgan Stanley both upped their forecasts for crude prices this week, while Goldman Sachs said the risks of prices overshooting its current targets are mounting.
"Our view is that prices are overheated, and will correct lower", SocGen said in a note.
"We're seeing the reality of strong demand and declining supplies".
Oil prices were little changed on Wednesday ahead of the release of US weekly petroleum inventory and production data.
USA production has fallen from 9.8 million barrels per day in December to 9.5 million bpd now.
However, most analysts still expect United States output to break above 10 million bpd soon.