* MSCI Asia ex-Japan fluctuates between gains and losses,

Kospi yo-yos

* Oil prices steady around $95 as Brent resumes trading

* Anthropic IPO, Google cash call renew hopes around AI

supply chain

By Gregor Stuart Hunter

SINGAPORE, June 2 (Reuters) - Asian stocks made a

cautious start to trading on Tuesday as uncertainty over whether

the ceasefire in the Middle East conflict capped the lift to

sentiment from renewed optimism around AI.

MSCI's broadest index of Asia-Pacific shares outside Japan

fluctuated between gains and losses as trading

commenced, last 0.5% lower, led by a 2% decline for Korean

shares after an initially higher open. S&P 500 e-mini

futures were down 0.3%, while in Japan, the Nikkei 225

slumped 0.7%.

"Conflicting news coming out of the Middle East left markets

whipsawing, with Iran stating that negotiations with the U.S.

have been suspended, only for President Trump to follow up in

recent hours with reassurances that talks are continuing 'at a

rapid pace'," analysts from Westpac wrote in a research note.

Brent crude held steady around $95 a barrel after

Lebanon announced a partial ceasefire between Hezbollah and

Israel on Monday, which could clear the path for renewed efforts

to end the three-month war between the United States and Iran.

Oil prices settled up more than 4% on Monday after reports

that Tehran had halted indirect negotiations with the U.S.

Overnight, the S&P 500 closed 0.3% higher after ISM's

manufacturing PMI rose to 54.0 in May from 52.7 the previous

month, beating expectations to reach the highest level in four

years, likely driven by businesses front-loading orders amid

rising prices and shortages because of the war with Iran.

"That the equity market is in boom mode is not up for

debate," despite higher energy prices and surging real interest

rates, said David Rosenberg, founder and president at Rosenberg

Research in Toronto, in a note to clients. "The S&P 500 is now

up nine weeks in a row, a streak we last witnessed in late

2023."

AI suppliers in Asia made gains after AI developer Anthropic

said it had confidentially filed for a U.S. initial public

offering, which could draw a trillion-dollar valuation.

Alphabet shares slipped 0.7% after the tech giant said

it is looking to raise $80 billion in equity offerings,

including an investment from Berkshire Hathaway, in an

aggressive push to fund expansion of its AI infrastructure.

The U.S. dollar index, which measures the greenback's

strength against a basket of six currencies, held steady at

99.18, firmly within the tight range it has sat in for the past

three weeks.

The yield on the U.S. 10-year Treasury bond was down 2.0

basis points at 4.455%. Gold was down 0.1% at $4,479.17.

In cryptocurrencies, bitcoin was down 0.2% at

$71,232.83, while ether was flat at $2,002.03.