International benchmark Brent crude futures were at $58.35 a barrel by 0249 GMT, down 18 cents, or 0.3%, from their previous settlement.
U.S. West Texas Intermediate (WTI) futures were at $54.29 per barrel, down 21 cents, or 0.4%, from their last close.
Both benchmarks fell last week, with Brent losing more than 5% and WTI falling about 2%.
“Oil prices are falling at the start of the trading week due to lower demand forecasts published last week and pessimism about a U.S.-China trade deal,” said Alfonso Esparza, senior market analyst at OANDA in Toronto.
The U.S.-China trade dispute rocked global equity markets last week, while a surprise build in U.S. crude stocks added downward pressure to oil prices, which have lost around 20% from their 2019 peaks reached in April.
Goldman Sachs said in a note on Sunday that fears of the U.S.-China trade war leading to a recession were increasing and it expected a trade deal between the two countries to happen before the 2020 U.S. presidential election.
Mounting signs of an economic slowdown and a ratcheting up of the trade row have caused global oil demand to grow at its slowest pace since the financial crisis of 2008, the International Energy Agency (IEA) said on Friday.
The Paris-based agency cut its 2019 and 2020 global oil demand growth forecast to 1.1 million and 1.3 million barrels per day (bpd), respectively.
Elsewhere, Russia’s oil production rose to 11.32 million bpd on August 1-8, up from 11.15 million bpd on average in July, according to two industry sources familiar with the energy ministry data.
In July, the Organization of the Petroleum Exporting Countries (OPEC) and its allies including Russia agreed to extend their supply cuts until March 2020 to prop up oil prices.
In a sign of lower production in the United States, the weekly U.S. oil rig count, an early indicator of future output, fell for a sixth week in a row as producers cut spending on new drilling and completions.
