By Christopher Johnson
LONDON (Reuters) - Oil prices rose on Thursday as a weaker dollar made fuel cheaper for holders of other currencies, and on hopes of a last-minute breakthrough that could keep Greece in the euro zone and help avoid a shock to European economic growth.
The dollar fell 0.65 percent to a one-month low against a basket of currencies after the Federal Reserve disappointed investors who had hoped for a clearer signal on when the U.S. central bank will lift interest rates.
European finance ministers were meeting in Luxembourg on Thursday for what could be the last best chance of a political rescue for Greece after other negotiations collapsed.
"The weak U.S. dollar is certainly one factor which can explain the price strength today," Carsten Fritsch, senior oil analyst at Commerzbank, told Reuters Global Oil Forum.
Brent crude for August rose $1.09 to a high of $64.96 a barrel before easing to around $64.10 by 1340 GMT.
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U.S. July crude was up 5 cents at $59.97 a barrel.
German Chancellor Angela Merkel said on Thursday it was still possible for Greece to reach an agreement with its international creditors - the European Union, International Monetary Fund and European Central Bank.
Oil prices slipped early on Thursday after data from the U.S. Energy Information Administration showed domestic gasoline stocks rose by 460,000 barrels last week, compared with analysts' expectations for a 314,000-barrel drop.
Gasoline demand across the northern hemisphere has been remarkably strong in recent months, pushing gasoline margins - the profit refiners make from turning crude oil into motor fuel - to their highest in nearly a decade.
Analysts say this is one reason why oil markets have been so strong despite a huge surplus of crude in many parts of the world and heavy over-production by key OPEC oil producers.
Prices have also been supported by worries that conflict in the Middle East could impact crude oil supply from the region.
Islamic State killed five policemen in a town near Iraq's biggest refinery in an attack that may help ease pressure on some of its fighters trapped in the strategically important facility, a security official said.
(Additional reporting by Meeyoung Cho in Seoul; Editing by Dale Hudson and Jason Neely)
