Pump jacks are seen at the Ashalchinskoye oil field owned by Russia's oil producer Tatneft near Almetyevsk, in the Republic of Tatarstan, Russia. Photograph:( Reuters )
Brent crude futures were down 3 cents by 0300 GMT at $64.20.
Crude prices were little changed on Monday as traders weighed geopolitical risks against the impact of the Sino-US trade war on the global economy, although last week's better-than-expected US jobs data offered some support.
Brent crude futures were down 3 cents by 0300 GMT at $64.20. US West Texas Intermediate (WTI) was up 6 cents at $57.57 a barrel.
"A very cautious open this morning supported by a better than expected (non-farm payrolls)," said Stephen Innes, managing partner at Vanguard Markets in Bangkok. "Traders remain incredibly cautious about the dimmer global economic overhang."
Both oil benchmarks fell last week as concerns about a slowing global economy outweighed risks to supply. Brent fell more than 3% and WTI shed more than 1.5%.
US job growth rebounded strongly in June, with government payrolls surging, the Labour Department's closely watched employment report showed on Friday, suggesting May's sharp slowdown in hiring was probably a one-off.
Employers added 224,000 jobs last month, the most in five months, the report showed.
But the US-China trade war has dampened prospects of global economic growth and oil demand.
The lack of concrete progress in resolving the acrimonious trade war between the United States and China, however, means the bar could be very high for the US Federal Reserve not to lower borrowing costs at its July 30-31 policy meeting.
White House Economic advisor Larry Kudlow has confirmed top representatives from the United States and China will meet in the coming week to continue trade talks.
Still, Japan's core machinery orders fell for the first time in four months in May, posing the biggest monthly drop in eight months in a worrying sign that global trade tensions are taking a toll on corporate investment.
Oil received some support from simmering tensions over Iran and after an extension last week to output cuts by OPEC and its allies.
Iran said on Sunday it will shortly boost its uranium enrichment above a cap set by a landmark 2015 nuclear deal, prompting a warning 'to be careful' from US President Donald Trump, who pulled out of the pact last year.
"Geopolitical risks remain plentiful, but the start of the week could see Iran worries ease," said Edward Moya, senior market analyst at OANDA.
Meanwhile, US energy companies this week reduced the number of oil rigs operating for the first time in three weeks as drillers follow through on plans to cut spending this year.