(Updates headline and prices throughout with U.S. markets, adds

fresh analyst quote)

* AI optimism and strong tech forecasts drive global

stock rally

* Oil slips, but Middle East tensions persist

* Euro zone core inflation rises, ECB rate hike expected

By Amanda Cooper and Chibuike Oguh

NEW YORK/LONDON, June 2 (Reuters) - Global stocks

rallied on Tuesday, buoyed by AI optimism, while oil prices and

bond yields fell on renewed hopes of a U.S.-Iran deal.

Brent crude futures fell 0.1% to just below $95 a

barrel, paring the previous session's sharp gains, after U.S.

President Donald Trump said talks with Iran continued.

His comments came despite a report that Tehran had suspended

indirect negotiations with Washington to end hostilities,

keeping investors cautious about efforts to end the three-month

war and underlining the fragility of an ongoing ceasefire.

AI ENTHUSIASM

Anthropic said on Monday it had confidentially filed for a

U.S. initial public offering, edging ahead of rival OpenAI in a

closely watched race to reach public markets. Google parent

Alphabet is also seeking to raise $80 billion in

equity to fund the expansion of its AI infrastructure.

"This speaks to the huge sums involved in keeping pace in

the AI arms race. It represents a significant shift from a

period of bumper free cash flow to going cap in hand to the

markets to help fund its expansion," Russ Mould, investment

director at AJ Bell, said.

On the economic front, U.S. job openings, a measure of labor

demand, increased more than expected in April, hitting the

highest level in nearly two years, according to Labor Department

data on Tuesday.

That came after data showed on Monday that U.S.

manufacturing beat expectations to hit a four-year high, likely

driven by firms front-loading orders amid rising prices and

supply concerns linked to the U.S.-Israeli war on Iran.

"The jobs data was significantly higher than expected and

you would think that it would have boosted rates but they didn't

go up," said Gerry Sparrow, chief investment officer at Sparrow

Capital Management.

"Employment is strong, which is a good thing for consumer

spending. So I think the market is healthy because of the jobs

data."

On Wall Street, all three indexes were trading higher after

losing ground in early trade. The Dow Jones Industrial Average

rose 0.30%, the S&P 500 rose 0.24%, and the Nasdaq

Composite rose 0.28%.

Europe's STOXX 600 was up 0.71%, as a strong

forecast from chipmaker STMicroelectronics lifted

technology stocks.

MSCI's gauge of stocks across the globe was

up 0.48% after hitting a fresh record high.

In Taipei, Nvidia ( NVDA ) CEO Jensen Huang said the company

had enough supply to support strong growth in central processing

units (CPUs) and graphics processing units (GPUs), but

acknowledged supply constraints remained a concern.

In currency markets, the dollar edged slightly lower. The

euro, still 1.5% below its level at the start of the war,

was last up 0.04% on the day at $1.16365.

The Japanese yen weakened 0.14% against the greenback

to 159.85 per dollar. Sterling strengthened 0.19% to

$1.3477.

Data showed euro zone core inflation at 2.5% year-on-year in

May, above expectations of 2.4% and April's 2.1%. Money markets

price in a quarter-point European Central Bank rate hike this

month, with at least one more by year-end.

The yield on the benchmark U.S. 10-year notes

fell 3 basis points to 4.447%. The yield on the

benchmark German 10-year Bunds fell 4 basis points

to 2.973%.

Gold rose 0.46% to $4,504.09 an ounce.