United States crude supplies fell by 1.3 million barrels last week, the American Petroleum Institute was said to report.
That effort has pushed oil prices above $50 a barrel in recent months, breathing life into US oil patches like the Permian Basin.
"Indeed, although the oil market will likely tighten throughout the year, overall non-OPEC production, not just in the US, will soon be on the rise again".
Saudi Arabia, de-facto leader of the Organization of the Petroleum Exporting Countries, has told other producers that it wants to extend a coordinated production cut beyond the first half of the year, the Wall Street Journal reported.
Brent crude futures were down 17 cents at $56.06 US a barrel, having touched a one-month high of $56.65 U.S.
The forecasts come as OPEC countries cut oil output in March more than anticipated.
OPEC is curbing its output by about 1.2 million barrels per day (bpd) from January 1 for six months, the first reduction in eight years, to get rid of a supply glut.
Based on direct communications with Nigeria, OPEC said the country's production levels were still around 1.269 million barrels per day.
Saudi Arabia and Russian Federation are leading the agreement by the Organization of Petroleum Exporting Countries and other producers to curtail oil supplies and end a three year surplus.
Oil prices of $60/bbl over the next three years and $70-$80 next decade will be roughly enough to balance the market, Ibrahim al-Muhanna, a former senior adviser to Saudi oil minister and now an independent consultant, says in prepared speech remarks. But it has kept supplies to Asia steady so far this year as it defends its market share in the world's fastest oil-demand growth region against other producers.
Reports have suggested that the cartel, prompted by kingpin Saudi Arabia, may extend the output cut deal by another six months when its members meet at the end of May.
Analysts and traders said long-term fundamentals remained strong and more stockpile draw-downs are likely as refiners exit maintenance season. If confirmed by U.S. Energy Information Administration figures on Wednesday, oil could get another boost.
Both benchmarks kicked off Thursday on a downbeat note after USA data on Wednesday showed domestic production jumped to its highest level in more than a year last week. Despite a bigger than expected drop in U.S. crude oil inventories, oil prices fell from their five-week highs, reached last week after the United States launched a set of airstrikes against the Syrian government.