The falls meant that both crude futures were at their lowest levels since mid-April
Oil prices fell sharply early on Monday after Greece rejected austerity measures demanded in return for bailout money and as China rolled out an unprecedented series of steps to prevent a full-blown stock market crash.
The result of the Greek referendum put in doubt its continued place in the single currency, pulling down the euro in early trading on Monday.
"With Greece reserves running low and no immediate bailout funds on the horizon, Greece is on a straight path out of the euro zone," said Howie Lee of Singapore-based brokerage Phillip Futures.
"Early morning indices' movements have shown the likes of the Nikkei and the STI to have fallen. The selling is likely to spread to European and US markets once they open."
In China, stock markets face a make-or-break week after officials rolled out a series of measures to prevent a full-blown stock market crash that would threaten the world's second-largest economy, although share prices rocketed on Monday in response to Beijing's measures.
International benchmark Brent futures were down around half a dollar at $59.80 per barrel at 0200 GMT, and U.S. crude futures were at $55.07 a barrel, down almost $2 since they last traded before the July 4 4 national holiday.
The falls meant that both crude futures were at their lowest levels since mid-April.
"Uncertainty over Greece is bearish for oil. It adds an extra negative factor on top of the turmoil in Chinese financial markets, the recent rise in U.S. drilling rigs, and a potential increase in Iranian oil supply," said Olivier Jakob, senior energy markets analyst at Petromatrix in Zug, Switzerland.
"The main implication is for euro/dollar and I think it will put additional pressure on the euro."
A strong greenback pressures oil markets as it makes dollar-traded fuel more expensive for countries using different currencies.
The euro slid more than 1 percent against the dollar and European stock and bond markets were poised to take a sharp hit with the resumption of trade on Monday, stunned European leaders called a summit for Tuesday to discuss their next move.
In China, brokerages and fund managers agreed to buy massive amounts of stocks to support markets which saw 30 percent falls since June, helped by China's state-backed margin finance company which in turn would be aided by a direct line of liquidity from the central bank.
Meanwhile, U.S. drilling increased for the first time after 29 weeks of declines, data showed on Thursday, the strongest sign yet that higher crude prices are coaxing producers back to the well pad.
Production in Russia and the Organization of the Petroleum Exporting Countries (OPEC) is also at near records.
