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Tightened supply following OPEC-led crude production cuts aided gains, along with positive signals from top central banks which sent global stocks higher after sharp losses in late 2018.
International Brent crude futures were at $61.76 per barrel at 1200 GMT, up 8 cents, while U.S. West Texas Intermediate (WTI) crude futures gained 23 cents to $52.82 per barrel.
WTI and Brent are set for their second week of gains, rising 10 percent and 8 percent respectively.
Markets were supported by hopes that an all-out trade war between Washington and Beijing might be averted. Three days of talks concluded this week with no concrete announcements, but higher-level talks may convene later this month.
"Sentiment is greatly improved, and trade talk optimism has helped boost risk appetite," Jasper Lawler, head of research at London Capital Group, said in a note.
Concerns about the global economy have kept markets in check, however, with signs mounting that China's growth in 2018 and 2019 would be the lowest since 1990.
Most analysts have downgraded their global economic growth forecasts below 3 percent for 2019, with some fearing a recession amid trade disputes and spiraling debt.
On the supply side, oil markets are receiving support from supply cuts led by the Organization of the Petroleum Exporting Countries and aimed at reining in a glut that emerged in the second half of 2018.
Lower oil exports from Iran since November, when U.S. sanctions against it resumed, have also supported crude.
Playing a key part in the emerging glut was the United States, where crude oil production soared by more than 2 million barrels per day (bpd) in 2018 to a record 11.7 million bpd.
Consultancy JBC Energy this week said it was likely that U.S. crude production was "significantly above 12 million bpd" by this month.
Abhishek Kumar, senior energy analyst at Interfax Energy in London, said higher oil prices so far this year "could well define a near-term trend despite uncertainties surrounding the U.S.-China trade talks."
"The implementation of the OPEC+ deal, together with potential for further falls in Iranian supplies, will also be bullish for prices."
(Reporting by Noah Browning in London; Additional reporting by Henning Gloystein in Singapore; Editing by Dale Hudson and Alexander Smith)