The price spread between USA benchmark WTI and Brent has widened to more than $7 a barrel.
U.S. West Texas Intermediate (WTI) crude futures were at $71.09 a barrel, up 13 cents and also not far off their November 2014 high of $71.89 a barrel reached last week.
OPEC crude production eased by 130,000 barrels per day (b/d) in April, to 31.65 mb/d, on further declines in Venezuela and lower output in Africa, the International Energy Agency (IEA) said in its Oil Market Report.
"You have the threat that a high enough price will start to activate the 7,700 drilled but uncompleted wells in the Lower 48 states", said Walter Zimmerman, chief technical analyst at ICAP TA.
The United States last week withdrew from an global nuclear accord with Iran and announced renewed sanctions against the country.
The tightening market has all but eliminated a global supply overhang which depressed crude prices between late 2014 and early 2017.
Current estimates by investment banks that see lowered Iranian and Venezuelan supply pushing up oil prices also assume that the global-and Chinese in particular-demand growth will continue to be strong.
OPEC figures published on Monday showed oil inventories in OECD industrialized nations in March fell to 9 million barrels above the five-year average, from 340 million barrels above the average in January 2017.
Despite these downward forces, the market retains support from OPEC and other producers' production cuts and USA sanctions on Iran.
The oil prices remain firm despite the output increase in USA oil rigs, with the experts estimating that the production may continue to rise for next over half-a-dozen months.
Oil settled higher Tuesday, with supply concerns tied to political unrest in the Middle East lifting prices for the global crude benchmark to its highest finish in 3 1/2 years.