Global fuel demand fell by about 30 percent in April, largely due to stay-at-home orders, and weak consumption is expected to keep excess supply on the market for months even as major global producers cut production from May 1.
But analysts said a swift move from those ends could help reduce supply glut at a faster pace.
Brent crude futures ended the trading session higher, 76 cents, or 2.9 percent, to settle at $ 27.20 a barrel.
US benchmark West Texas Intermediate crude futures rose 61 cents, or 3.1 percent, to settle at $ 20.39 a barrel.
The benchmarks continued to rise in post-settlement trading, extending their gains to more than 5 percent.
American investment bank Goldman Sachs said it was increasingly optimistic about the rise in crude prices next year due to lower crude production and a partial recovery in oil demand.
The bank raised its forecast for the year 2021 for the world price of Brent crude to 55.3 dollars per barrel from 52.50 dollars.
It also increased its estimate for West Texas Intermediate crude to $ 51.38 a barrel from $ 48.50 in its previous forecast.