According to Reuters, the Organization of Petroleum Exporting Countries (OPEC) is considering holding a meeting this week to discuss extending unprecedented production cuts beyond the end of this June.
Brent crude settled unchanged at $ 37.84 a barrel, on the first trading day of the August contract as the nearest maturity contract.
West Texas Intermediate crude futures for July delivery recorded $ 35.53 a barrel, up 4 cents or 0.1% by 6:29 GMT.
The decline comes after prices for the nearest maturity month for Brent and West Texas recorded their strongest monthly gain in years in May.
The gains were supported by the decline in OPEC crude production to its lowest level in 20 years, with demand expected to recover as more countries emerge from the comprehensive closures imposed to combat the Corona virus.