U.S. West Texas Intermediate (WTI) futures were down 15 cents, or 0.2 percent, at $72.79. The U.S. rig count, an early indicator of future output, was up by five in the week to July 6, according to General Electric Co's Baker Hughes energy services firm.
Brent crude futures fell 25 cents, or 0.3 percent, to $77.14 per barrel by 0317 GMT from their last close.
US crude inventories probably declined by 5 million barrels last week, according to a Bloomberg survey.
Stocks of gasoline and middle distillates such as heating oil and diesel fuel also drew, the survey showed.
Traders are paying attention to the escalating trade dispute between the United States and China although the current products caught in the tariff war are not energy-related.
South Korea has suspended all buying of Iran crude and superlight crude, more commonly known as condensate after the US stepped up pressure on Iran crude buyers to stop importing its crude, Reuters reports, citing unnamed sources familiar with developments.
The latter have soared in the last two years to around 400,000 barrels per day in July, worth around $1 billion at current market prices.
The cancellations mean South Korea will import no Iranian oil in August, the first month of zero imports since August 2012 when South Korean buyers put Iranian oil purchases on hold before getting a waiver to import limited amounts of Iran crude, Reuters added.
"Venezuela.will lose another 400,000 bpd by year-end with production going to below 1 million bpd", FGE said, adding that another 300,000 bpd of Libyan capacity was disrupted.
Monica Malik, chief economist, Abu Dhabi Commercial Bank, welcomed the UAE's decision to hike output later this year as it will bring stability in the oil market and also improve government revenues from hydrocarbon sector. While Saudi Arabia is facing mounting pressure from Trump to do more, America's oil sanctions on Iran and trade frictions with China are adding to uncertainties with planned US tariffs on Chinese goods set to start Friday.
"Iran's exports are some 2.7 million bpd, including condensate", it noted.