"Investors may start pricing in a much higher risk premium", said Hussein Sayed, chief market strategist at FXTM.
Brent crude futures were at US$69.62 per barrel at 0651 GMT, up 96 cents, or 1.4 per cent, from their last close. Crude futures have recently tracked with equities.
Chinese and US officials have also softened their rhetoric over their trade spat, easing worries over the potential for a slowdown in demand for oil. "The odds of a coordinated response to the chemical-weapon attack in Syria (http://www.marketwatch.com/story/trump-issues-warning-after-dozens-killed-in-apparent-chemical-weapons-attack-in-syria-2018-04-08) is making short selling more unsafe".
Intermediate for May delivery rose as much as US$1.41 to US$64.83 a barrel on the New York Mercantile Exchange, and was at US$64.46 as of 8:48am local time on Tuesday.
Also supportive to crude prices was the weakness of the US dollar.
The statement addresses one of the grievances of US President Donald Trump, who has requested US trade officials last week to consider imposing another $100 billion in tariffs on Chinese products. The total count now adds up to 808, the highest level since March 2015, suggesting that the USA will be having more supply to come.
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Meanwhile, news that Saudi Arabia is aiming for an $80 oil price offered further support, according to Flynn.
Oil prices also traded higher Tuesday amid a report from Bloomberg News, which said that Saudi Arabian officials were seeking $80 a barrel on Brent crude to support the valuation of its energy giant, Aramco, before its initial public offering. "Usually, what the Saudis want, the Saudis get", said Flynn.
The oil market got another boost later on in the day after data from the USA government said domestic production would be slightly lower in 2018 than previously - but not by much.
U.S. WTI crude futures were up 25 cents at $62.31 a barrel. It also forecast average retail gasoline prices of $2.74 a gallon for the summer driving season, up from $2.41 for the summer of 2017.
US West Texas Intermediate (WTI) crude futures for the May contract edged higher by 1.2 percent to $64.22 per barrel, while global benchmark Brent futures for June delivery climbed by 1.2 percent to $69.53 per barrel. That would be a second week of declines after a surprise drop of 4.6 million barrels a week earlier.
Monthly oil reports are also due out from the Organization of the Petroleum Exporting Countries on Thursday and the International Energy Agency on Friday.