U.S. WTI crude futures were up 25 cents at $62.31 a barrel.

Oil prices fell about 2% on Friday after US President Donald Trump threatened new tariffs on China, reigniting the fear of a trade war between the world's two largest economies that could hurt global growth.

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.

Brent crude for June delivery traded 1.8% lower Friday, at $67.07 a barrel.

In physical oil markets, Opec's number two producer Iraq said on Monday that it was keeping prices for its crude supplies in May steady.

Then Chinese President Xi Jinping showed signs of relenting in the trade spat with the United States, promising to open up China's economy, including lowering tariffs on cars and enforcing intellectual property of foreign firms-something that the Trump administration has been eyeing for some time.

Market players now looked ahead to fresh data on US commercial crude inventories to gauge the strength of demand in the world's largest oil consumer and how fast output levels will continue to rise.

Traders said weekly USA fuel inventory data would provide further market guidance.

"The market is now concerned for the escalating China-U.S. trade war tensions".

"In addition to the risk of protectionism, there has been a significant change in the Trump administration that has raised risks of potential sanctions on key oil exporting countries including Iran, Venezuela and Russian Federation", U.S. bank JPMorgan said.

Turning to data, unofficial figures from the American Petroleum Institute suggest that both crude and gasoline stocks were higher last week (the consensus expected stocks to keep falling). "However, oil market fundamentals are tightening and oil prices looks set to be squeezed higher as long as OPEC+ sticks to its cuts". Only Russia pumps more crude out of the ground, at nearly 11 million bpd.

Oil markets have generally been supported by healthy demand as well as supply restraint led by the Organization of the Petroleum Exporting Countries (OPEC).

"Oil prices remain rangebound with WTI oil right in the middle of the $60-$65 per barrel range that has largely held since January of this year", said William O'Loughlin, investment analyst at Australia's Rivkin Securities.

However, soaring U.S. crude production C-OUT-T-EIA, 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.