The world's benchmark crude was up 85 cents, or 1.1%, at $77.97 a barrel by 11:22 a.m. ET (1522 GMT).
Oil held near $71 a barrel on heightened political risks in the Middle East following unrest in Gaza and the return of sanctions against Iran.
Elsewhere, supply concerns have been mounting over the last week after President Donald Trump the USA pulled out of the Iran nuclear deal - a move that reimposes sanctions on Iranian barrels. Investors are watching whether OPEC and its allies such as Russian Federation intend to end output cuts and increase production if renewed American measures restrict the Persian Gulf state's exports.
OPEC is to focus on oil inventory, rather than price.
Oil prices hit a 3-1/2-year high on Tuesday, supported by tight supply and planned US sanctions against Iran that are likely to restrict crude oil exports from one of the biggest producers in the Middle East. Brent crude oil LCOc1 reached $79.22 a barrel, up 99 cents and its highest since November 2014.
USA light crude was 15 cents lower at $70.81 a barrel, also not far off its highest since November 2014, in a volatile session. Total volume traded was about 37% below the 100-day average.
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WTI light sweet oil was up 57 cents at USD71.52 a barrel, having touched the highest in 4 years.
The surge in oil prices comes at a time of tight supply amid record Asian demand and voluntary output restraint totaling 1.8 MMBPD by the Organization of the Petroleum Exporting Countries and non-OPEC producers, including Russian Federation.
OPEC figures published on Monday showed that oil inventories in OECD industrialised nations in March fell to 9 million barrels above the five-year average, down from 340 million barrels above the average in January 2017.
The Organisation of the Petroleum Exporting Countries (Opec), has not restricted the number of barrels available but has not made up for the loss of barrels from Iran.
Rosneft's oil and gas condensate output in the first quarter was down 1.2 percent year on year because of the global supply pact with OPEC, the company said on Monday. With more than 1 200 people wounded by live fire, it was the deadliest day in Gaza since Hamas's last war with Israel in 2014.