Rising production from OPEC as well as the US also weighing on prices
Greece, as expected, was not able to repay 1.6 billion euros it owed to the IMF, in what was the largest missed payment in the Fund's history.
Greece's default pushed up the dollar versus the euro, with the stronger greenback pressuring crude prices as it increases dollar-denominated oil import prices for countries using different currencies.
Front-month Brent crude futures were trading at $63.09 per barrel at 0116 GMT, down 50 cents from their last settlement. US crude futures fell 65 cents at $58.82 per barrel.
Analysts said rising production from the Organization of Petroleum Exporting Countries (OPEC) as well as in the United States also weighing on prices.
"Iraqi crude production climbed to a record level this month, with OPEC crude oil output estimated to have reached 32.1 million barrels per day against a target of 30 million barrels per day," ANZ said in a morning note.
Overall OPEC supply rose to a three-year high of 31.60 million barrels per day (bpd) in June, up from 31.30 million bpd in May, according to a Reuters survey.
The group has raised output by more than 1.3 million bpd since it decided in November 2014 to defend market share rather than prices.
A final deal between world powers and Iran over Tehran's nuclear work could add to supplies. A June 30 deadline for a nuclear deal that could let Iran export more crude into an oversupplied market has been extended by a week to July 7.
In the United States, crude production rose 9,000 barrels a day to 9.701 million barrels a day in April, the highest since May 1971, the U.S. Energy Information Administration said in monthly data released Tuesday.
Crude inventories rose by 1.9 million barrels in the week to 468.9 million, compared with analyst expectations for a decrease of 2.000 million barrels.
However, demand was also up with refinery crude runs rising by 77,000 barrels per day, API data showed.
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