By Georgina McCartney

HOUSTON (Reuters) -Oil settled higher on Wednesday as ongoing tensions in the Middle East lent support to prices, but news that interest rate cuts could start as late as December capped gains, following the Federal Reserve's statement concluding its two-day meeting.

Brent crude futures settled 68 cents, or 0.83%, higher at $82.60 a barrel, with U.S. West Texas Intermediate (WTI) crude futures up 60 cents, or 0.77%, to $78.50.

Prices had eased more than 2% last week after OPEC and its allies said they would phase out output cuts starting from October.

Palestinian militant group Hamas has proposed numerous changes, some unworkable, to a U.S.-backed proposal for a ceasefire with Israel in Gaza, U.S. Secretary of State Antony Blinken said on Wednesday, adding that mediators were determined to close the gaps.

At a press conference with Qatar's prime minister in Doha, Blinken said some of the counter-proposals from Hamas, which has ruled Gaza since 2007, had sought to amend terms that it had accepted in previous talks.

The war has yet to materially affect global oil supply, but investors have priced in the risk, boosting crude futures prices.

Meanwhile, investors were left disappointed after the Federal Reserve pushed out the start of rate cuts to perhaps as late as December, with officials projecting only a single quarter-percentage-point reduction for the year amid rising estimates for what it will take to keep inflation in check.

U.S. consumer price data, published on Wednesday, had reinforced expectations of a Fed rate cut in September. Fed Chair Jerome Powell will hold a press conference later on Wednesday.

"It will be interesting to see what Powell says, I don’t think there is any doubt that they will leave rates where they are," said Ben McMillan, a fund manager for IDX Advisors.

Higher borrowing costs tend to dampen economic growth, and could, by extension, limit oil demand.

"The market is holding its breath right now," said Tim Snyder, economist at Matador Economics.

"If Powell talks outside of what the Fed publishes, there could be a little discord within the policy committee as to their direction on interest rates," Snyder added.

Elsewhere, European Central Bank Vice President Luis de Guindos said the ECB must move "very slowly" in reducing interest rates, because of huge uncertainty over the inflation outlook.

U.S. crude stocks posted a surprise build last week, up by 3.7 million barrels to 459.7 million barrels, compared with expectations of a 1 million barrel-draw, the Energy Information Administration (EIA) said on Wednesday.