SINGAPORE, June 14 (Reuters) - Oil prices eased on Friday as markets evaluated the impact of U.S. interest rates staying higher for longer than anticipated, but crude benchmarks headed for their best week in more than two months after solid projections for crude and fuel demand.

Brent crude futures were down 34 cents, or 0.4%, at $82.41 a barrel by 0344 GMT. West Texas Intermediate (WTI) U.S. crude futures lost 41 cents, or 0.5%, to trade at $78.21 a barrel.

However, Brent and the U.S. benchmark gained over 3% for the week - the best week since April 5.

The Organization of Petroleum Exporting Countries (OPEC) stuck to a forecast for relatively strong growth in global oil demand for 2024 and Goldman Sachs projected solid U.S. fuel demand this summer.

This helped reverse losses in the previous week which were driven by an agreement by OPEC and its allies, together called OPEC+, to start unwinding output cuts after September.

"Overall, this week can be characterised as a recovery effort for oil," said Tim Waterer, chief market analyst at KCM Trade based in Australia.

"I wouldn't be surprised to see oil prices head higher from here whilst the demand outlook continues to look rosier. Much may depend on how the northern hemisphere summer demand picture plays out."

Providing further support to the market, Russia pledged to meet its output obligations under the OPEC+ pact, after saying it exceeded its quota in May.

However, the price rally this week cooled after the U.S. Federal Reserve held interest rates steady and pushed out the start of rate cuts to as late as December.

Meanwhile, the International Energy Agency said in a report on Wednesday it sees oil demand peaking by 2029, levelling off at around 106 million barrels per day (bpd) towards the end of the decade.

On the downside, concerns over economic outlook grew after the Fed's view on rate cut, but that said, to the extent that this buoys the U.S. dollar, it could offer a measure of support to Brent, BMI analysts wrote in a note.

Market focus is also on the ongoing Gaza ceasefire talks, which, if resolved, would alleviate concerns about potential disruptions in oil supply from the region.

The U.S. is very concerned that hostilities on the Israel-Lebanon border could escalate to a full-out war, a senior U.S. official said, saying that specific security arrangements are needed for the area and a ceasefire in Gaza is not enough. (Reporting by Ashitha Shivaprasad in Singapore, addititonal reporting by Katya Golubkova in Tokyo; Editing by Michael Perry)