Brent crude oil futures were at $71.80 per barrel at 0120 GMT, up 38 cents, or 0.5 percent, from their last close.
U.S. West Texas Intermediate (WTI) crude futures were up 39 cents, or 0.6 percent, at $66.61 a barrel.
Traders said oil markets were receiving general support due to a sense that there were high risks of supply disruptions, including a potentially spreading conflict in the Middle East, renewed U.S. sanctions against Iran and falling output as a result of political and economic crisis in Venezuela.
“With so many potential supply disruptors in play and few signs that the current market upheaval will end any time soon, traders continue to pay the geopolitical risk premium,” said Stephen Innes, head of trading for Asia-Pacific at futures brokerage OANDA in Singapore.
“Oil prices should remain bid … at least through the Iran nuclear deal deadline (May 12) if not for the remainder of 2018,” he added.
Oil markets have generally been well supported this year, with Brent up by around 16 percent from its 2018-low in February, due to healthy demand which comes as the producer cartel of the Organisation of the Petroleum Exporting Countries (OPEC) leads supply cuts aimed at tightening the market and propping up prices.