Brent crude futures rose $ 1.17 to $ 44.45 a barrel by 0904 GMT, and were on track to post the largest daily increase since mid-June, while West Texas Intermediate U.S. crude gained 19 cents to $ 41, the highest daily level in a month, up nearly 2.6 percent.
The prices have revived an agreement among European Union leaders on a 750 billion euro ($ 859 billion) fund to support economies affected by the Corona virus, boosting fuel demand forecasts.
In other markets, global stocks and the euro recorded their strongest levels since March on Tuesday.
The agreement allows the European Commission to raise billions of euros from financial markets on behalf of the 27 member states, in an unprecedented solidarity in nearly seven decades of European integration.
Prices received support from promising data on a vaccine for the virus on Monday, which boosted confidence that the vaccine could be produced even if its production would take global time.