The increases came after a more than 2 percent rise on Monday, which recovered the 2 percent slump on Friday, when oil prices also suffered their worst weekly declines in two months amid growing concerns over a trade war between the world's two biggest crude consumers.
In other energy news Tuesday, the U.S. Energy Information Administration raised its 2018 and 2019 price forecasts for WTI and Brent crude.
Oil prices on Wednesday eased away from 2014 highs reached the previous session as escalating Middle East tensions were offset by increasing inventories and production in the United States.
"It's not so much "risk on/risk off", as it is "trade war on/trade war off" and, at the moment, we're 'trade-war off, '" London Capital Group's Jasper Lawler said.
In post-settlement trading, Brent hit $71.34, its highest since December 2014.
Iran, meanwhile, struck a defiant tone on Monday, saying Western allies may have regrets should U.S. President Donald Trump break the United Nations -backed nuclear agreement when sanctions go under review in May.
The West Texas Intermediate (WTI) for May delivery rose 2.09 USA dollars to settle at 65.51 dollars a barrel on the New York Mercantile Exchange, while Brent crude for June delivery added 2.39 dollar to close at 71.04 dollars a barrel on the London ICE Futures Exchange. The total count now adds up to 808, the highest level since March 2015, suggesting that the U.S. will be having more supply to come.
The Saudis want oil prices near $80, in part to support the valuation of state-owned energy giant Aramco ahead of its initial public offering, Bloomberg News reported Tuesday (https://www.bloomberg.com/news/articles/2018-04-10/saudi-arabia-is-said-to-signal-ambition-for-80-oil-price?utm_medium=social&utm_campaign=socialflow-organic&utm_content=markets&cmpid%3D=socialflow-twitter-markets&utm_source=twitter), citing people who have spoken to delegates from the Organization of the Petroleum Exporting Countries and oil market participants.
OANDA's Innes said the API report had "temporarily taken a bit of wind out of the market".
The oil price is up by almost 2% so far this year, thanks to healthy demand and supply restraint led by Opec, which started in 2017 to rein in oversupply and prop up prices.
In the oil market, US crude inventories may have fallen by 1.4 million barrels last week, according to a Bloomberg survey before government data on Wednesday. Analysts anticipated a decline in crude and gasoline inventories.
The American Petroleum Institute will publish its storage data later on Tuesday.
May natural gas ended at $2.656 per million British thermal units, down 1.4%.