Brent prices have lost more than 9pc in the past week, with US President Donald Trump vowing to impose new tariffs on Chinese imports and China making further moves against US agricultural cargoes.
The United States also responded to a decline in China's yuan on Monday by branding the country a currency manipulator.
International benchmark Brent futures were up 18 cents at $59.99 a barrel by 1005 GMT, having dipped earlier in the session to their lowest since Jan. 14 at $59.07.
West Texas Intermediate crude futures rose 25 cents to $54.94 per barrel.
"This morning's slight price recovery is hardly worthy of mention. Concerns about demand and the escalating trade conflict are still keeping the oil market in a stranglehold," Commerzbank analyst Carsten Fritsch said in a note.
"As far as the oil market is concerned, there are two key questions: 1) Why should China carry on buying US crude oil? and 2) Why should China continue to adhere to the US sanctions when it comes to buying Iranian oil?"
Global equities hit a two-month low and Brent fell more than 3pc on Monday as traders worried the dispute between the world's two biggest oil buyers would dent demand, helping to prompt Tuesday's short-covering.
London's main stock market index dropped for a sixth straight session on Tuesday.
"It's difficult for oil to hold (up) when you have such moves in equities," Petromatrix analyst Olivier Jakob said.
Oil prices could find some support later on Tuesday, with a Reuters poll showing US crude oil inventories were expected to have fallen for an eighth consecutive week.
The American Petroleum Institute is set to release its weekly inventory data at 4:30 p.m. EDT (2030 GMT), with official government numbers to follow on Wednesday.
On the supply side, Iran has threatened to block all energy exports out of the Strait of Hormuz, through which a fifth of global oil traffic passes, if it is unable to sell oil as promised by a 2015 nuclear deal in exchange for curbing uranium enrichment.
Britain on Monday joined the United States in a maritime security mission in the Gulf to protect merchant vessels after Iran seized a British-flagged vessel.