The Organization of the Petroleum Exporting Countries, Russia and other producers, an alliance known as OPEC+, are reducing output by 1.2 million bpd from January 1 for six months.
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.
Saudi output dropped to its lowest in over two years, boosting compliance with supply cuts to 153 percent, according to IEA estimates.
"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.
Warns demand fell in developed OECD countries by 0.3 million bpd.
Meanwhile, the latest EIA report showed that the USA crude inventories rose 7 million barrels to 456.6 million barrels in the last week, their highest since November 2017.
Venezuela is an OPEC member but exempt from the cuts as it struggles with political turmoil, sanctions and repeated power blackouts.
The producer group's supply cuts have been aimed largely at offsetting record crude production in the United States.
The combined supply cuts have helped to drive a 32 percent rally in crude prices this year to almost $72 a barrel, prompting U.S. President Donald Trump to call on OPEC to ease its market-supporting efforts.
The concerted push to lower prices has been successful, with the price of Brent crude rising from $50 a barrel in December to above $71 in early April.
Worldwide benchmark Brent futures were at $71.13 a barrel at 1201 GMT, down $0.6 from their last close.
The West Texas Intermediate for May delivery gained 0.31 USA dollar to settle at 63.89 dollars a barrel on the New York Mercantile Exchange, while Brent crude for June delivery climbed 0.72 dollar to close at 71.55 dollars a barrel on the London ICE Futures Exchange.
US crude inventories rose seven million barrels to 456.6 million barrels in the last week, their highest since November 2017, the Energy Information Administration said on Wednesday.
Saudi Arabia can add more oil to the market without adjusting production quotas since the kingdom's output in March was some 500,000 bpd below its OPEC target, the source added.