Brent for August settlement dropped as much as 90 cents, or 1.8 percent, to $49.73 a barrel on the London-based ICE Futures Europe exchange.
Trump's withdrawal from the Paris agreement, the landmark 2015 global pact to fight climate change, drew condemnation from Washington's allies and many in the energy industry - and sparked fears that US oil production could expand more rapidly than it is now.
"This could lead to a drilling free-for-all in the US and also see other signatories waver in their commitments", said Jeffrey Halley, senior market analyst, OANDA. "Demand growth has slowed somewhat recently, and with USA production growing strongly, there doesn't seem to be much room for OPEC production to grow in 2018".
OPEC and non-OPEC members last week agreed to extend production cuts for a period of nine months until March, but stuck to production cuts of 1.8 million bpd agreed in November previous year.
Russian Deputy Prime Minister Arkady Dvorkovich said on Friday he did not think that the global output cut agreement would be altered should prices go lower.
Saudi Energy Minister Khalid al-Falih said further oil output cuts could be needed in the future but that OPEC and other leading producers would assess the market situation in July, Russia's TASS news agency reported on Saturday.
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Despite this, Brent futures are still down about 7 percent from their open on May 25, when OPEC announced it would extend its production cut into 2018.
Faced with lingering glut woes, the oil cartel discussed last week reducing output by a further 1 to 1.5 percent, and could revisit the proposal should inventories remain high, according to sources.
Official data showed crude inventories in the United States, the world's top oil consumer, fell sharply last week as refining and exports surged to record highs.
It's no wonder, then, that global oil prices have remained subdued and even announcements like the 6.4-million-barrel draw in U.S. oil inventories that the EIA announced yesterday have failed to have any impact.
However, U.S. crude production rose to 9.34 million bpd last week, up almost 500,000 bpd from a year ago. All this growth stems from shale drilling, as the more modest growth from Gulf of Mexico deepwater fields is offsetting declines from other U.S. conventional oilfields.
"The market is testing OPEC for firmer action", said Olivier Jakob, managing director at consultant Petromatrix GmbH in Zug, Switzerland.
Production cuts by OPEC and its partners are taking longer than expected to eliminate the surplus as USA shale drillers boost production with surprising speed.