Brent crude futures rose 17 cents to $US60.92 a barrel by just after midnight on Monday, Greenwich Mean Time, paring earlier losses. US West Texas Intermediate crude was meanwhile at $US57.43 a barrel, up 11 cents.
The United States snatched Maduro from Caracas at the weekend. Trump said Washington would take control of the oil-producing nation and that the US embargo on all Venezuelan oil remained in full effect.
The US strike on Venezuela to extract the country's president inflicted no damage on the country's oil production and refining industry, two sources with knowledge of operations at state oil company PDVSA said at the weekend.
In a global market with plentiful oil supply, analysts said any further disruption to Venezuela's exports would have little immediate impact on prices.
"We see ambiguous but modest risks to oil prices in the short-run from Venezuela depending on how US sanctions policy evolves," Goldman Sachs analysts led by Daan Struyven said in a January 4 note, keeping its 2026 oil price forecasts unchanged.
Helima Croft, RBC Capital's head of commodities research, said: "Certainly, we think full sanctions relief could unlock several hundred kb/d (thousand barrels per day) of production over a 12-month period in an orderly transition situation."
"However, all bets are off in a chaotic change of power scenario like what occurred in Libya or Iraq," she added.
A top Venezuelan official declared on Sunday that the country's government would stay unified behind Maduro.
The Organisation of the Petroleum Exporting Countries and their allies, together called OPEC+, decided to hold their output on Sunday.
Analysts are also watching Iran's reaction after Trump threatened on Friday to intervene in a crackdown on protests in the OPEC producer, ratcheting up geopolitical tensions.
At least 16 people have been killed during a week of unrest in Iran, rights groups said on Sunday, as protests over soaring inflation spread across the country.
