By 1530 GMT, Brent crude futures were up $ 2.07, or 10%, to $ 22.54 a barrel.
US West Texas Intermediate crude futures rose $ 3.80, or 31%, to $ 16.10 a barrel, after tumbling below zero last week.
The increase in crude stocks in the United States fell short of expectations, amid hopes for better demand as some European countries and American cities moved to ease restrictions.
Crude prices are under pressure from a decline in fuel demand around 30% worldwide.
The major oil producing countries agreed in mid-April to cut production by about 10 million barrels per day, while shale oil producers and other major suppliers are also cutting.
The main Saudi index increased 1.5%, with Al-Rajhi Bank shares adding 2.7% and Jabal Omar Development 6%.
Shares of oil giant Aramco closed up 0.8%.
In Dubai, the index rose 0.3% as Emaar Real Estate rose 1.1%, while Emaar Development jumped 4.1%.
However, Dubai Islamic Bank came down 0.8% and has a $ 425 million exposure to NMC Health Hospital Management.
Reuters quoted three banking sources as saying that UAE banks that have exposure to the struggling health care company have avoided allocations between 25 and 50% of the company’s debt, which exceeds two billion dollars.
The Abu Dhabi index gave up early gains, to close flat. The shares of First Abu Dhabi Bank, the country’s largest bank, increased 0.4%, while Abu Dhabi Commercial Bank fell 0.5%, and its exposure to NMC was 981 million dollars.
In Qatar, the stock market rose 1.2%, and most stocks, including the Commercial Bank, closed 4% higher.
Outside the Gulf, the main Egyptian index rose 1.2% thanks to Commercial International Bank, which jumped 3.8%.