"There seems to be a slightly more conciliatory tone coming from both sides" in the trade spat, Neil Atkinson, head of the oil-markets and industry division at the International Energy Agency, said in a Bloomberg television interview.
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. Following Xi's speech, Asian stocks and US futures jumped in Asian morning trading.
The president met with military officials in the White House Monday to discuss the administration's response to an alleged chemical weapons attack carried out by Syrian President Bashar Assad 's government against its own people.
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.
In the United States, drillers added 11 rigs looking for new production in the week to April 6, bringing the total count to 808, the highest level since March 2015, General Electric's (GE.N) Baker Hughes energy services firm said on Friday.
But the USA decision to impose tariffs on $50 billion of Chinese goods a week later sent the price to a two-week low.
With Chinese markets closed last Thursday and Friday, Shanghai crude futures ISCc1 played catch-up on Monday, dropping 0.2 percent to around 401.4 yuan ($63.73) per barrel.
Meanwhile, news that Saudi Arabia is aiming for an $80 oil price offered further support, according to Flynn.
Oil prices rose on Thursday, holding onto a late-session rally the previous day, buoyed by the US government data showing a surprise drawdown in crude stockpiles. "Usually, what the Saudis want, the Saudis get", said Flynn.
Beyond the trade dispute, oil markets are also concerned about the potential of renewed U.S. sanctions against some significant oil producers.
And "Russia with sanctions in place will also need to comply as they cant afford to risk a break in the price of oil", he said. Record U.S. crude production is also threatening efforts by the Organization of Petroleum Exporting Countries and its allies to curtail output and drain a global glut.
The EIA's weekly petroleum supply data are due Wednesday.
"China is the main importer (after Canada) of US crude oil, to the tune of about 400,000 barrels per day", Petromatrix said, Reuters reported.
Gasoline stocks fell by 1.1 million barrels, compared with analysts' expectations for a 1.3 million barrels drop.