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.

The U.S. Treasury Department authorized Iranian sales of crude ​oil and petrochemical and petroleum products through August 21, easing decades-old sanctions, as the United States pushes toward a final peace deal with Iran in return for commitments on nuclear inspections and free transit through the Strait of Hormuz.

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

The Dow Jones Industrial Average rose 0.29%, the ⁠S&P 500 fell 0.37% and the Nasdaq Composite fell 1.32%.

Europe's STOXX 600 index rose 0.58%. MSCI's gauge of stocks across the globe fell 0.03%.

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 5.78 basis points to 4.509%.

The apparent progress in U.S.-Iranian discussions pushed Brent crude futures to settle lower by 3.38% to $77.90 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 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 0.11% at $1.3244.

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

The euro eased 0.36% to $1.1427, after hitting a three-month low on Friday at $1.1418.

The dollar was up 0.19% at 161.58 yen, with only the threat of Japanese intervention preventing the currency from 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 0.17%. Spot ​gold rose 0.72% to $4,190.17 an ounce.

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