Brent crude was up 6 cents at $61.01 a barrel by 0339 GMT, while U.S. West Texas Intermediate (WTI) crude was up 5 cents at $56.35 a barrel.

Both contracts spent the Asian trading session ticking either slightly higher or lower. Brent is set to mark its fourth weekly gain, while U.S. crude is headed for a second weekly rise.

Beijing and Washington on Thursday agreed to hold high-level talks in early October in Washington, cheering investors hoping for an end to the trade war between the world's two biggest economies that has brought tit-for-tat tariff hikes, chipping away at economic growth.

The prolonged dispute had a dampening effect on oil prices, although they have risen over the year, helped by production cuts led by the Organization of the Petroleum Exporting Countries and its allies, including Russia, to drain inventories.

"Upside potential for crude oil futures will remain limited, however, as strong U.S. production and demand-side concerns cap bullish gains for the current term," said Benjamin Lu, commodities analyst at Phillip Futures in Singapore.

He also cited "subdued economic momentum, global trade uncertainties and rising market risks" for reasons to expect that U.S. crude would be range-bound between $55-$60 over the third quarter.

U.S. crude and product inventories fell last week, with crude drawing down for a third consecutive week despite a jump in imports, the Energy Information Administration (EIA) said.

Crude stocks dropped 4.8 million barrels, nearly double analysts' expectations, to 423 million barrels, their lowest since October 2018.

Oil prices on Thursday soared more than 2% after the EIA report, although they gradually trimmed gains as investors are not entirely convinced that the Sino-U.S. trade talks will yield results.