By Henning Gloystein
Brent crude oil futures were at $71.69 per barrel at 0326 GMT, up 27 cents, or 0.4 percent, from their last close.
U.S. West Texas Intermediate (WTI) crude futures were up 32 cents, or 0.5 percent, at $66.54 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 Organization of the Petroleum Exporting Countries (OPEC) leads supply cuts aimed at tightening the market and propping up prices.
U.S. OUTPUT SOARS
Beyond OPEC's production restraint and concerns about supply disruptions, the main market driver in oil has been the United States, where crude production has soared by almost a quarter since mid-2016 to 10.53 million barrels per day (bpd), largely thanks to a booming shale industry.
Only Russia pumps out more oil currently at almost 11 million bpd.
"U.S. shale producers have been quietly capitalising on higher oil prices with increasing rig counts seen. A staggering amount of 73 rotary rigs have been placed since January 2018," said Benjamin Lu of Phillip Futures in a note on Tuesday.
"As such, we expect a softening in crude oil prices as markets adjust from a bullish streak," he added.
The American Petroleum Institute (API) is due to publish weekly U.S. fuel inventory data later on Tuesday while official government data, including on production, is due from the U.S. Energy Information Administration (EIA) on Wednesday.
(Reporting by Henning Gloystein; Editing by Joseph Radford and Kenneth Maxwell)
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