Oil prices have fallen due to dollar prices slumped, making the crude futures cheaper for buyers in other currencies.
The value of the dollar dropped 0.5% to a one-month low after Federal Reserve voted to keep interest rates unchanged.
Brent crude for August increased $1.02 to a high of $64.89 a barrel, while the US July crude rose 70 cents at $60.62 a barrel, Reuters reported.
The dollar value weakened after the Federal Reserve disappointed investors who were expecting a positive signal on when the US central bank will increase interest rates.
Oil prices also increased due to hopes of a last-minute breakthrough to keep Greece in the eurozone.
The meeting of European finance ministers in Luxembourg on Thursday would serve as a political rescue for Greece after its other negotiations failed.
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German Chancellor Angela Merkel said that Greece still has chances to reach an agreement with its international creditors including the European Union, International Monetary Fund as well as the European Central Bank.
Worries surrounding crude oil supply from Middle East due to attacks also led to rise in prices.
The impact of tropical depression Bill on oil prices were negative as it drenched major part of Texas on Wednesday, without affecting oilfields in the Gulf of Mexico and near the coast.