(Updates prices throughout, adds latest news, moves US futures

higher, adds Euro zone manufacturing survey)

* Oil prices surge nearly 3% as Gulf hostilities threaten

Strait of Hormuz reopening

* AI demand drives global stocks to record highs despite

Middle East tensions

* Fed speakers, payroll data in focus as rate hike odds

remain split

By Wayne Cole and Amanda Cooper

SYDNEY/LONDON, June 1 (Reuters) - Global stocks held

steady near record highs on Monday as the AI boom continued to

drive demand, offsetting news of fresh attacks in the Gulf that

challenged optimism about a reopening of the Strait of Hormuz

and drove up oil prices.

Iran and the United States said they had both carried out

strikes on military targets, and each accused the other of

acting aggressively as diplomatic efforts to end three months of

war drag on.

While negotiators from Washington and Tehran are apparently

working to hammer out a deal, U.S. President Donald Trump had

been silent on their progress until posting that everyone should

"just sit back and relax".

Speaking on Saturday, Defense Secretary Pete Hegseth said

the U.S. was ready to restart attacks on Iran if a deal could

not be reached. On Monday, news emerged that U.S. forces struck

Iranian targets over the weekend and Tehran had hit back, while

Kuwaiti defences were reportedly intercepting missile and drone

strikes.

Brent crude futures rose nearly 3.3% to $94.12 a

barrel, which in turn prompted a selloff in government bonds,

which have been hurt by growing expectations that interest rates

will rise to combat any spikes in inflation.

S&P 500 futures firmed 0.3%, while Nasdaq futures

firmed 0.3% after the benchmark indexes hit records last

week.

The MSCI All-World index was flat on the

day, close to record highs, as markets from Tokyo to Seoul

traded at or near all-time peaks, underpinned by avid demand for

anything AI-related.

"Even though there have been attacks from both sides, the

market is holding on to the fact that negotiations are ongoing,

and an elusive Iran/U.S. deal to end the war in the Middle East

and to reopen the Strait of Hormuz will still be found," XTB

research director Kathleen Brooks said.

"As the focus switches to a raft of macro releases later

this week, investors will need to watch how this plays out, and

any delay in reaching a deal could knock market sentiment," she

said.

The power of the AI rush was underlined by data showing

South Korea's exports grew at the strongest annual rate in more

than four decades in May to hit a record $87.75 billion.

Nvidia ( NVDA ) boss Jensen Huang kicks off the Computex

trade show in Taiwan on Monday with a speech about AI in which

he is expected to expound on his company's latest product

efforts as well as the island's central role in the industry.

PAYROLLS AHEAD

European stocks were down marginally on the day, as

gains in energy shares were offset by losses in airlines and

defence shares.

The inflationary pulse from oil continued to hamper bond

markets as U.S. 10-year yields rose 1.2 basis points

to 4.465%, while yields on 10-year German debt rose

5 bps on the day to 2.98%.

"Market needs an agreement to open the Strait of Hormuz, to

provide the next leg higher in equities and lower in rates,"

wrote Mohit Kumar, chief European economist at Jefferies, in a

note.

"As we enter June, focus would turn to the central bank

meetings over the coming weeks," he said.

A host of Fed members are set to speak this week, while

major U.S. data include the ISM survey of manufacturing and the

May payrolls report on Friday.

Market forecasts are for a solid rise of 85,000 in

employment, keeping the jobless rate steady at 4.3%. Anything

stronger would likely see the odds of a hike narrow further.

"The lineup of Federal Reserve speakers throughout the week

should continue to reinforce a balanced two-way policy approach,

with officials remaining open to both rate hikes and rate cuts

depending on incoming data," Pepperstone chief market strategist

Chris Weston said.

"Consequently, expectations may build that the Fed gradually

moves away from its easing bias and towards a more neutral

policy stance in the months ahead."

Markets imply a 50-50 chance the Federal Reserve will have

to hike rates by year-end, which has helped the dollar remain

firm against a range of currencies, most notably, the Japanese

yen.

The dollar was up another 0.1% against the yen at 159.44

, just below the 160 barrier that many believe could

trigger another round of official intervention to boost the

Japanese currency.

Elsewhere, growth in euro zone manufacturing lost momentum

in May as demand for goods stagnated and supply-chain

disruptions linked to the Middle East war pushed input costs to

their highest in four years, a survey showed on Monday.