U.S. WTI crude futures were at $62.31 a barrel at 0643 GMT, up 25 cents, or 0.4 percent, from their previous settlement.
Crude prices at the end of last week closed down roughly 2%, capping their worst week in two months, as the USA threatened new tariffs on Chinese imports and Beijing responded in kind.
Brent crude futures rose $2.56 to $71.21 a barrel, a 3.7 percent gain, by 3:12 p.m. EDT.
Light, sweet crude for May delivery rose $1.29, or 2%, to $64.71 a barrel on the New York Mercantile Exchange, trading at a one-week high.
Concerns of a prolonged trade dispute between the world's two biggest economies and uncertainty over the supply and demand balance of global oil markets have resulted in volatile yet range-bound recent trading.More news: BJP functionary, in Mumbai for party rally, dies on board train
Brent crude's three year plus high came as geopolitical concerns in the Middle East - coupled with easing US-China trade tension, a weaker dollar and a small decline in forecasts for US oil production - saw the oil bulls emerge after being battered on Friday.
"There are headlines of a US carrier group heading to the Middle East, the Saudis are looking for $80 Brent crude, and this is ahead of API inventories", said Roberto Friedlander, head of energy trading at Seaport Global Securities.
Both equity and oil markets rallied after the speech, while supposed safe havens such as U.S. Treasurys and gold slipped, supporting Wall Street's thesis that a trade war between the economic superpowers is increasingly unlikely.
The American Petroleum Institute is due to publish oil storage data later on Tuesday while official data from the US Energy Information Administration (EIA) is due on Wednesday.
"The market is now concerned for the escalating China-U.S. trade war tensions". "However, oil market fundamentals are tightening and oil prices looks set to be squeezed higher as long as OPEC+ sticks to its cuts".More news: Celtics routed by Raptors
However, soaring USA crude production, which has jumped by a quarter since mid-2016 to 10.46 million barrels per day (bpd), is threatening to undermine OPEC's efforts to tighten the market and prop up prices.
The Saudis want oil prices near $80 to help support the valuation of Saudi Aramco ahead of its IPO, Bloomberg reports.
The U.S. late a year ago overtook Saudi Arabia as the world's second-biggest crude producer.
OPEC and other producers, including Russian Federation, agreed to cut output by about 1.8 million barrels per day (bpd) in November last year to slash global inventories to the five year-average.More news: US slaps sanctions on Putin's allies
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