World oil prices fell on Tuesday as traders mostly took their cue from the rebounding US dollar and output remained strong, dealers said.

US benchmark West Texas Intermediate (WTI) for delivery in July fell $1.69 cents from Friday's close to $58.03 a barrel.

In London trade, Brent North Sea crude for July lost $1.80 to $63.72 per barrel.

The dollar powered to a fresh eight-year high of 123.3 yen on Tuesday, while the euro, slipping to $1.0875, was weighed by growing concerns about Greece's bailout talks as a repayment deadline looms.

"Crude oil prices remained under pressure... as the US dollar continues its strong upside momentum," said Myrto Sokou, senior energy analyst at the Sucden brokerage in London.

The stronger greenback makes crude more expensive for buyers using weaker currencies.

Bart Melek of TD Securities noted as well that the OPEC cartel, at more than 31 million barrels a day, is still producing well over its quota cap, keeping the market generously supplied.

"The other factor beside the US dollar, is that there is concern about the demand side particularly from Asia, China specifically," he said.