Global benchmark Brent futures were at 71.44 USA dollars per barrel at 0424 GMT, down 29 cents, or 0.4 percent, from their last close.
Oil markets have been lifted by more than a third this year by supply cuts led by OPEC, U.S. sanctions on oil exporters Iran and Venezuela, plus escalating conflict in fellow OPEC member Libya.
"Electrical outages added a further hurdle to Venezuelan production, which fell by 290,000 barrels per day in March to 732,000 barrels per day".
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. Macroeconomic uncertainties can take their toll on oil demand, the IEA said.
"Russia has started talks about an oil production rise as it can hardly follow the OPEC+ deal", said another Russian energy source.
"We maintain our forecast of 1.4 Mmbpd (in 2019 oil demand growth), but accept that there are mixed signals about the health of the global economy, and differing views about the likely level of oil prices", IEA said.
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On the demand side, Chinese data showed exports rebounded last month, driving USA and euro zone bond yields to three-week highs and helping offset weaker imports and reports of another cut in German growth forecasts.
Venezuela reported a production figure of 960,000 bpd, down by a massive 472,000 bpd, as power outages and United States sanctions cripple the South American oil producer. It hit a session high of $64.65 earlier in a fresh attempt by long-oil hedge funds to reach the $65 target.
USA sanctions and power outages pushed OPEC member Venezuela's crude output to a long-term low of 870,000 bpd, IEA says.
OPEC, Russia and other non-member producers are reducing output by 1.2 million bpd from January 1 for six months.
At the last OPEC meeting in Vienna, the group's members agreed to slash output by 812,000 bpd, with Russian Federation and nine other non-OPEC allies committing to a cut of 383,000 bpd for the first six months of 2019.
In February, the oil reserves of the OECD countries remained at 16 million barrels above the five-year average.