Brent crude, the global benchmark, was down 19 cents at $77.20 a barrel while USA crude slipped 2 cents to $72.92.
US West Texas Intermediate (WTI) crude futures CLc1 were down 16 cents, or 0.2 percent, at $73.98 per barrel.
NAB said its oil price forecasts "point to Brent spending the next few months largely in the mid-to-high $70s (per barrel) range, although meaningful OPEC-Russia output increases could push prices lower later in the year and higher United States shale production should impose an upside limit on WTI".
"Increased Saudi crude availability that is being enhanced by reduced OSPs (official selling prices) into Europe and other regions is providing a strong counter against curtailed Libyan export activities", Ritterbusch wrote.
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 United States tariffs on Chinese goods set to start tomorow.
The U.S. bank warned that supply threats were "threatening a sharp further rise in prices and global economic growth".
According to analysts, escalating tensions between China and the US, with the two largest economies in the world implementing tariffs $34 billion on their respective imports and the threat of more action, could weigh on crude prices and soften demand expectations.
Saudi Arabia's objective, revealed at the OPEC meeting in June, has been to stabilise production and prices around current levels.
The leader of Saudi Arabia, OPEC's biggest member, has assured Trump that the kingdom can raise oil production if needed, and that the country has 2 million barrels per day of spare capacity that could be deployed to help cool oil prices to compensate for falling output in Venezuela and Iran.
Saudi Arabian Oil Co will change its Asia crude pricing benchmark by replacing Platts' Oman assessment with the Dubai Mercantile Exchange's Oman futures from October 1.
Following his comments, oil prices fell on July 5.
After all the tough talk by the USA about countries cutting oil purchases from Iran to zero by November 4, India will have a chance to discuss the issue of crucial energy imports when a team of officials from the state and treasury departments visits the country this month.