GLOBAL MARKETS-Stocks steady, oil falls as rate worries offset Iran talks optimism

(New throughout, updates prices and adds analyst comment)

* S&P 500 edges lower and EU stocks gain

* Oil prices fall as Iran and US say progress made in talks

* Sterling and UK bonds rise after PM Starmer resigns

By Chibuike Oguh

NEW YORK, June 22 (Reuters) - Global stocks were mostly flat on Monday while oil prices fell, as optimism over progress in U.S.-Iran talks was offset by expectations of higher interest rates that pushed U.S. Treasury yields up.

U.S. Vice President JD Vance said in Switzerland that Iran agreed to allow nuclear inspectors into the country, with conversations over the inspections possibly beginning as soon as this week.

Officials from Qatar and Pakistan had said progress was made on a roadmap to reach a final deal in 60 days.

On Wall Street, the benchmark S&P 500 and the Nasdaq were lower on the day, dragged down by communication services and consumer discretionary stocks. The Dow was higher.

The Dow Jones Industrial Average rose 0.23%, the S&P 500 fell 0.37% and the Nasdaq Composite fell 1.09%.

Europe's STOXX 600 index was last up 0.56%. MSCI's gauge of stocks across the globe was up by 0.02%.

Asian stocks climbed overnight, supported by the apparent progress in peace talks. MSCI's broadest index of Asia-Pacific shares outside Japan closed higher by 0.88%.

Markets are being driven by the Fed's hawkish outlook and reduced expectations that new Fed chair Kevin Warsh would move to begin cutting rates, said Gerry Sparrow, chief investment officer at Sparrow Capital Management.

"The market was somewhat surprised by the new Fed chair's action as it was under the expectation that he was going to be a little easier on rates," Sparrow said.

The Federal Reserve last Wednesday held interest rates steady, but policymakers expect a hike in borrowing costs later this year amid growing concerns about inflation lodged above the U.S. central bank's 2% target.

The yield on benchmark U.S. 10-year notes rose 4.39 basis points to 4.495%.

The apparent progress in discussions pushed Brent crude futures lower by 3.8% to $77.44 a barrel, far below its May peak of $126.41.

"The progress in peace talks is good but the only negative surprise was the new Fed wasn't a little bit more accommodative during its most recent announcement," Sparrow said.

UK POUND RISES AFTER STARMER RESIGNS

The pound and UK bonds rose after Prime Minister Keir Starmer announced his resignation, paving the way for Britain's seventh leader in 10 years.

The pound reversed earlier losses and was up 0.16% at $1.325 while the 10-year gilt yield fell 3.37 basis points to 4.808%.

Former Manchester Mayor Andy Burnham is the favourite to succeed Starmer, but investors said a key question for nervy UK bond markets would be who becomes finance minister.

The euro eased 0.29% to $1.14375, after hitting a three-month low on Friday at $1.1418.

The dollar was flat at 161.38 yen, with only the threat of Japanese intervention preventing the currency rising to 2024's 40-year high of 161.96.

The dollar index, which measures the greenback against a basket of currencies including the yen and the euro, rose 0.08%. Spot gold rose 0.56% to $4,183.19 an ounce.

(Reporting by Chibuike Oguh in New York; Additional reporting by Wayne Cole and Harry Robertson, Editing by William Maclean)