US benchmark West Texas Intermediate for July delivery dropped 33 cents to USD 59.63 a barrel compared with Friday's close.
Brent North Sea crude for July shed $1.47 to stand at USD 62.40 a barrel in late London deals.
Markets are "closely tracking the Greek debt crisis and the ongoing negotiations between Iran and the big six powers", said Sanjeev Gupta, analyst at business consultancy firm EY.
Crunch negotiations between Athens and its creditors fell apart on Sunday, fuelling fears the cash-starved government was heading irreversibly into the financial abyss with a huge IMF debt payment due at the end of the month.
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Investors are also focusing on Iran ahead of a June 30 deadline for the Islamic republic and world powers to come to an agreement on curbing Tehran's nuclear programme.
Six global powers -- Britain, China, France, Germany, Russia and the United States -- are trying to nail down a deal to curb Iran's nuclear ambitions by reducing its stockpiles of enriched uranium and mothballing some of its sites.
Iran has the world's fourth-largest oil reserves but its exports have fallen from more than 2.2 million barrels per day in 2011 to about 1.3 million because of the sanctions.