New York-traded crude was up 62 cents, or 1%, at $64.20 per barrel by 11:00 AM ET (15:00 GMT).
Venezuelan production dropped due to United States sanctions, which added to an already deep economic and political crisis in the country, while Iranian production is also expected to drop further as a result of the U.S. sanctions which are to be tightened in May.
These concerns outweigh the optimism derived from the ongoing OPEC supply cuts and the U.S. sanctions on Iran and Venezuela that helped the prices reach five-month tops earlier this week.
OPEC, Russia and other non-member producers are reducing output by 1.2 million bpd from January 1 for six months.
The rig count fell for the past four months as independent exploration and production companies cut spending on new drilling to focus on earnings growth instead of increased output.
The March figure is down from 30.56 million bpd in February, largely on a huge fall in production from Venezuela and Saudi Arabia.
The report pointed to a slightly under-supplied market in 2019 if OPEC kept pumping at March's level.
The latest IEA monthly oil market report showed that the Venezuelan oil output plummets to 870,000 bpd on outages and sanctions, as cited by Reuters.
"(Oil markets will remain tight) as long as Saudi Arabia continues to back the production cut deal as aggressively as it has done so far", said Ole Hansen, head of commodity strategy at Saxo Bank.
"An increase is on the table, yes, if prices went to $80 and higher", this OPEC source said. "It all depends on where prices are by the end of May and June".
The prospective initiative from OPEC was reportedly encouraged by the recent rally in prices and because extending its production cuts with Russian Federation and other allies could over-tighten the market (the cartel agreed with allies to withhold 1.2 million barrels per day (bpd) of crude since the start of 2019, and its output fell 550,000 bpd in March to 30.1 million bpd).