SINGAPORE, June 6 (Reuters) - Oil extended gains from the previous session on Thursday amid growing expectations the Federal Reserve will cut interest rates in September, though prices were capped on the back of higher U.S. inventories and an OPEC+ plan to increase supply.

Brent crude futures rose 31 cents, or 0.40%, to $78.72 a barrel by 0330 GMT, while U.S. West Texas Intermediate crude futures climbed 41 cents, or 0.55%, to $74.48.

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.

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

The oil benchmarks were still headed for weekly declines of about 4% as of Thursday, weighed down by the latest supply decision from the Organization of the Petroleum Exporting Countries and allies.

The group 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.

"We believe the OPEC+ move to unwind the 2.2 million barrels per day in the final quarter of 2024 will add further pressure to benchmark prices," said Emril Jamil, senior analyst for crude at LSEG Oil Research.

Bearish sentiments are also expected to prevail on expectations of weaker demand as inventory builds, said Jamil.

Saudi Arabia has also cut its official selling prices (OSP) for July crude, a document seen by Reuters showed on Wednesday. The move came amid falling Middle East crude benchmarks and weaker profit margins for Asian refiners.

Meanwhile, 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. (Reporting by Jeslyn Lerh in Singapore; Additional reporting by Colleen Howe in Beijing; Editing by Jamie Freed)