(Updates to U.S. market open)

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

* Hopes for US-Iran agreement continue

* Yen stable after spikes, intervention jitters persist

By Lawrence Delevingne and Sophie Kiderlin

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.