GLOBAL MARKETS-Stocks edge up, oil prices continue pullback on peace optimism

* U.S. stocks edge up as oil prices fall ​again

* Hopes for US-Iran ⁠agreement continue

* Yen stable after spikes, intervention jitters persist

May 7 (Reuters) - Global stocks mostly held their gains on Thursday while oil prices sank again on optimism over a U.S.-Iran peace deal, even as the fate of ​the ‌critical Strait of Hormuz appeared unresolved. On Wall Street, the previous session's record highs held, with the S&P 500 little changed, and the Nasdaq Composite up 0.27%. The Dow ⁠Jones Industrial Average rose 0.12%. Europe's STOXX 600 was 0.37% lower, having jumped 2.2% on Wednesday, ⁠while MSCI's broadest index of Asia-Pacific shares outside Japan ​hit a fresh all-time high. It was last up 1.75%. Japan's Nikkei crossed 62,000 for the first time as trading resumed after an extended holiday weekend. MSCI's All-Country World Index rose 0.37% to trade around record highs.

While the Middle East situation was uncertain, "the momentum is going in a good direction" and markets ​had taken note ‌of it, Lombard Odier Chief Economist Samy Chaar said.

"So the oil price is down from its highs, which is obviously relieving pressure on yield curves and bond yields, and that is great news for equity valuation and makes currencies move a bit," he said.

A strong earnings season and a relatively robust macroeconomic environment added to a positive market mood, Chaar added.

TRUMP PREDICTS SWIFT END TO WAR The United States and Iran are edging toward ​a limited, temporary agreement to halt their war, sources and officials said on Thursday, with a draft framework that would stop the fighting but leave the ‌most contentious issues unresolved. Brent crude fell almost 4% to $97.38 a barrel, having tumbled nearly 8% on Wednesday.

Even after that slide, Brent is still around 40% above its late-February level, when the conflict began, ‌while 10-year Treasury yields have surged — a reminder of the strain higher energy costs continue to put on the global economy.

On the day, 10-year Treasury yields were last down by 2 basis points to 4.334%.

Nick Twidale, chief market strategist at ATFX Global, said the market was wrestling with execution risk, "both ​in terms of whether a deal is finalised and how quickly disrupted flows would normalize even if it is."

Rocketing oil prices whacked global markets in March but a fragile ceasefire ‌and prospect of a deal have spurred a risk-on rally since April that has been fuelled by strong tech earnings reports.

S&P COMPANIES SET FOR ROBUST PROFIT GROWTH S&P 500 companies are on track for their strongest profit growth in more than four years, while blowout results from Samsung , SK Hynix and ⁠TSMC have reinforced ⁠the upbeat tone in Asia. Investors await the U.S. non-farm payrolls report on Friday, with jobs expected ‌to have increased in April by 62,000 after rebounding 178,000 in March, a Reuters survey of economists shows. In currency markets, the euro nudged higher and last fetched $1.1773. Sterling was slightly higher ​at $1.3624 as UK local elections came into ​focus. The dollar index, which measures the U.S. currency against six units, was a touch lower at ‌97.85. The yen remained in the spotlight after spikes in recent sessions prompted market speculation that Tokyo had intervened to support the long-battered currency. The yen was little changed at 156.36 per dollar, having hit a 10-week high of 155 on Wednesday.