(Reuters) -Oil was set to fall this week with the Iran-Israel ceasefire holding and easing concerns over Middle East supply risks, although prices rose on Friday as the summer driving season ramped up fuel demand in the United States.

Brent crude futures rose 34 cents, or 0.5%, to $68.07 a barrel by 0111 GMT. U.S. West Texas Intermediate crude gained 33 cents, or 0.51%, to $65.57 a barrel.

The benchmarks were set to fall about 12% for the week.

Oil futures hit their lowest in more than a week on Tuesday after U.S. President Donald Trump said a ceasefire had been agreed between Iran and Israel. 

Oil prices inched up on Thursday, though, as U.S. government data showed crude oil and fuel inventories fell last week, with refining activity and demand rising. [EIA/S]

"The market is starting to digest the fact that crude oil inventories are very tight all of a sudden," said Phil Flynn, senior analyst with the Price Futures Group. 

Also supporting oil prices, the dollar index sank to a three-year low on a report that President Donald Trump was planning to choose the next Federal Reserve chief early, fuelling fresh bets on U.S. interest rate cuts.

A weaker dollar makes oil less expensive for holders of other currencies, increasing demand and supporting prices.

Shortly before oil settled on Thursday, Prime Minister Benjamin Netanyahu said the outcome of Israel's war with Iran presented opportunities for peace that his country must not waste, easing concerns of continuing supply risks.