Brent crude was unchanged at $37.84 a barrel, in the first day of trading in the contract with August as the front month.
WTI crude futures for July delivery were at $35.53 a barrel, up 4 cents, or 0.1%, by 0629 GMT.
OPEC+ is set to discuss a short extension of its current output cuts, according to a delegate, as the cartel considers bringing forward its next meeting a few days to June 4.
The coalition is considering extending the current curbs for one to three months, the delegate said.
Still, tensions between the United States and China weighed on global financial markets, while traders are also keeping an eye on riots over the weekend that have engulfed major U.S. cities. (FIS)