Oil prices rebounded Tuesday as traders expected that Greece won't exit the Eurozone.

Earlier on Tuesday Greece confirmed that Athens would not repay the loan installment due to International Monetary Fund Tuesday.

Greek Prime Minister Alexis Tsipras' office said in a statement Tuesday that it proposed a two-year debt deal with the European Stability Mechanism in a last-minute bid to avert the countdown to default and a possible Grexit.

And Tsipras was ready to travel to Brussels, Belgium, later to discuss the proposal with European partners.

At the same time, the European Commission said it had offered a deal to Greece to stave off a crisis.

Traders thought Greece still have chance to reach a last-minute deal with European Commission, the probability of Grexit is still low.

The West Texas Intermediate for August delivery moved up 1.14 U. S. dollars to settle at 59.47 U.S. dollars a barrel on the New York Mercantile Exchange, while Brent crude for August delivery increased 1.58 dollars to close at 63.59 dollars a barrel on the London ICE Future Exchange.