* South Korea leads Asian stocks higher, S&P futures firm

* Oil gains as Gulf talks drag on, Israel pushes into

Lebanon

* Bonds ease ahead of US factory, jobs data and Fed speak

(Adds South Korean exports, Samsung stock, China data)

By Wayne Cole

SYDNEY, June 1 (Reuters) - Asian share markets firmed on

Monday as the boom in all things AI continued to drive demand,

offsetting a lack of progress in Gulf peace talks that

challenged optimism on a re-opening of the Strait of Hormuz and

lifted oil prices.

While negotiators from Washington and Tehran are apparently

working to hammer out a deal, President Donald Trump has been

notably silent on their progress. 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.

Tensions in the region were not helped by an Israeli push

further into Lebanon in the battle against the Iranian-backed

Hezbollah militant group.

"While uncertainties remain, the acute risk phase for the

global economy should be over if tankers can begin moving

again," said Michael Feroli, head of U.S. economics at JPMorgan.

"Still, not everything would return to its pre-conflict

place - oil prices are likely to remain elevated for some time,

as inventories get rebuilt and the supply infrastructure in the

Middle East is repaired."

Indeed, the lack of news nudged Brent up 2.1% to $93.02 a

barrel, while U.S. crude added 2.6% to $89.61.

Asian share markets remain underpinned by demand for

semiconductors and AI-related gear, with Japan's Nikkei

up a further 1.1%, having risen almost 5% last week to all-time

highs.

South Korea rose 4.4%, after surging 8% last week,

while Taiwan climbed almost 6% last week. MSCI's

broadest index of Asia-Pacific shares outside Japan

added 1.6%.

Shares in Samsung Electronics ( SSNLF ) jumped almost 10%

on Monday adding to gains on Friday after it said it had started

shipping samples of its latest high-bandwidth memory (HBM) chip

to customers.

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.

Chinese blue chips dipped 0.3%, having been

restrained recently by a lacklustre economy, with a survey

showing factory activity stalled in May.

COUNTDOWN TO PAYROLLS

For Europe, EUROSTOXX 50 futures dipped 0.1%, while

DAX futures were flat and FTSE futures lost

0.2%.

S&P 500 futures were up 0.3%, while Nasdaq futures

firmed 0.5% after hitting records last week.

Yet the gains have been narrowly based with the AI-linked

big 10 companies making up 40% of the S&P 500 and only 21 stocks

of the 500 making record highs. While tech stocks climbed almost

16% in May, consumer discretionary and healthcare managed little

more than 2%, and consumer staples lost more than 3%.

The inflationary pulse from oil continues to hamper bond

markets as U.S. 10-year yields rose 3 basis points

to 4.470%. Markets imply a 50-50 chance the Federal Reserve will

have to hike rates by year-end to prevent rising prices from

getting baked into inflationary expectations.

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

major 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 market's hawkish outlook has kept the dollar broadly

steady, with the Japanese yen and the euro hampered by those

regions' reliance on energy imports.

The dollar was a shade firmer on the yen at 159.45

, but bulls were wary of risking Japanese intervention

on a break of the 160.00 barrier.

The euro stood at $1.1645, having spent the past

week hemmed in between $1.1585 and $1.1661.

In commodity markets, gold was 0.3$ softer at $4,523 an

ounce, having found little support as a safe haven or as

a hedge against inflation.