By Nicole Jao

NEW YORK (Reuters) -Oil prices edged higher on Thursday as crude inventories in the United States fell on higher demand as summer driving season ramped up, while concerns over Middle East supply risks eased, offsetting some gains.

Brent crude futures settled 5 cents, or 0.07%, higher to $67.73 a barrel. U.S. West Texas Intermediate crude gained 32 cents, or 0.49%, to $65.24 a barrel.

Both benchmarks climbed nearly 1% on Wednesday, recovering from losses earlier in the week after data showed resilient U.S. demand. Brent futures were trading below their close of $69.36 on June 12, the day before Israel started airstrikes on Iran.

The U.S. driving season had started slowly but was now stoking demand, ANZ analysts said.

"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.

U.S. crude oil and fuel inventories fell in the week to June 20 as refining activity and demand rose, the Energy Information Administration said on Wednesday. [EIA/S]

Crude inventories fell by 5.8 million barrels, the EIA said, exceeding analysts' expectations in a Reuters poll for a 797,000-barrel draw.

Also supporting oil prices, the dollar index, which measures the greenback against a basket of currencies, sank to a three-year low as a report that President Donald Trump was planning to choose the next Federal Reserve chief early fuelled fresh bets on U.S. rate cuts.

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

However, signs of easing Middle East supply risks offset some gains.  

Shortly before oil markets 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.

Trump hailed the swift end to war between Iran and Israel and said Washington would likely seek a commitment from Tehran to end its nuclear ambitions at talks with Iranian officials next week.

Trump also said on Wednesday that the U.S. was maintaining maximum pressure on Iran - including restrictions on sales of Iranian oil - but signalled a potential easing in enforcement to help the country rebuild.

"(The) rapid push for a ceasefire suggests that President Trump remains sensitive to high oil prices, in our view, potentially capping the geopolitical risk premium even as the conflict may linger," Citi said in a note on Thursday.

(Reporting by Nicole Jao in New York, Enes Tunagur in London, Yuka Obayashi in Tokyo and Emily Chow in Singapore; Editing by David Evans, Joe Bavier, Barbara Lewis, Ed Osmond and Cynthia Osterman)