Brent crude futures were down 21 cents at $63.25 a barrel by 0850 GMT. Prices rose 1.6pc last week.
US West Texas Intermediate crude was down 7 cents at $56.13 a barrel. WTI gained 1pc last week.
Economic growth in the United States slowed less than expected in the second quarter with a boom in consumer spending, strengthening the outlook for oil consumption.
But non-US growth is slowing faster, due partly to the country's trade war with China over the last year.
"Fragile economic growth caused by the confrontational and protectionist US trade policy is having a profound impact on oil demand and oil demand growth," PVM analyst Tamas Varga said.
US and Chinese negotiators meet this week for the first time since trade talks broke down in May, but expectations are low after President Donald Trump said China might not want to sign a trade deal until after the 2020 US election.
"Even though the crude oil supply picture is fundamentally tight ... and geopolitical risks front and centre, the market remains extremely bearish around demand risks due to the escalation in protectionist trade policies and the risk of additional punitive tariffs," said Emily Ashford, director of energy research at Standard Chartered.
Traders and investors are also focussed on meetings of major central banks - including the US Federal Reserve, which is expected to lower interest rates.
Crude prices were still supported by supply risk as tensions remain high around the Strait of Hormuz, the world's most important oil passageway.
Britain warned Iran on Monday that it must follow international rules and release a British-flagged vessel seized in the Gulf this month.
Defying the pressure, Iran's Revolutionary Guards published new footage of the seizure of the tanker.
US energy companies last week reduced the number of oil rigs operating for a fourth week in a row, putting the rig count down for an eighth consecutive month.