BEIJING, June 6 (Reuters) - Oil rose in early Asian trading on Thursday on rising expectations the Federal Reserve will cut interest rates in September, and as the market rebounded from a selloff related to growing U.S. inventories and an OPEC+ plan to increase supply.

Brent crude futures rose 27 cents, or 0.34%, to $78.68 a barrel by 0103 GMT, while U.S. West Texas Intermediate crude futures rose 36 cents, or 0.49%, to $74.43.

Nearly two-thirds of economists are now predicting an interest rate cut in September, according to Reuters' May 31-June 5 poll, offsetting recent bearish supply news.

Lower interest rates decrease the cost of borrowing, which can incentivise economic activity and boost oil demand.

Traders are also viewing the selloff on the back of U.S. inventory data as "overdone", ANZ analysts said in a note.

Prices initially fell in early trading on Wednesday after U.S. crude stocks jumped by 1.2 million barrels in the week to May 31, compared with analysts' estimates for a draw of 2.3 million barrels, data from the U.S. Energy Information Administration showed.

But prices later rebounded to end the session up 1% on the view the selloff had been too sharp and on the growing interest rate optimism.

However, the Fed's interest rate path is far from a foregone conclusion. U.S. services sector activity, which accounts for the vast majority of the country's economic output, returned to growth in May following a contraction in the previous month, in a shift that could potentially weaken the case for interest rate cuts.

Oil prices had fallen after the Organization of the Petroleum Exporting Countries and allies agreed on Sunday to extend most of their oil output cuts into 2025 but left room for voluntary cuts from eight members to be unwound gradually, beginning in October.

In the Middle East, Hamas leader Ismail Haniyeh said on Wednesday the militant group would demand a permanent end to the war in Gaza and Israel's withdrawal as part of a ceasefire plan in what appeared to be a rebuttal to a peace proposal put forward by President Joe Biden, while Israel announced a new military campaign against Hamas.

British security firm Ambrey said on Thursday a Greek-owned bulk carrier was allegedly targeted by Yemen's Houthis while travelling northbound in the Red Sea.

However, geopolitical risks have taken a backseat to market fundamentals recently. (Reporting by Colleen Howe; Editing by Jamie Freed)