(Recasts with preliminary close of trading, adds analyst

comment)

* Alphabet dips on plans to raise $80 billion for AI

buildout

* Marvell ( MRVL ) jumps on Nvidia's ( NVDA ) CEO calling it the next

trillion-dollar company

* Software shares down following a strong rebound rally

By Stephen Culp and Medha Singh

NEW YORK, June 2 (Reuters) - The S&P 500 and the Dow

closed modestly higher on Tuesday as risk appetite driven by AI

fervor was counterbalanced by tensions arising from U.S.-Iran

talks to reopen the Strait of Hormuz and end the months-long

war.

Gains in most of the 11 major S&P sectors kept the S&P 500

and the Dow in the green, with the small-cap Russell 2000

outperforming its larger-cap peers. The Nasdaq ended the session

essentially unchanged.

Small-cap stocks have been some of the biggest beneficiaries

of the ongoing enthusiasm surrounding artificial intelligence

stocks, which provided some upside muscle. The Philadelphia SE

Semiconductor Index advanced on the day.

The Software & Services Index, battered in recent

months over worries of AI disruption, closed in negative

territory.

Strong results from Hewlett Packard Enterprise ( HPE ) and a

funding commitment from Alphabet reinforced confidence

in the AI buildout.

"The market is kind of muted at the surface level, but there

is a lot going on under the hood, and that describes much of

this year," said Mike Dickson, head of portfolio management at

Horizon Investments in Charlotte, North Carolina. "There's some

massive dispersion in the whole AI infrastructure ecosystem."

"Markets could be in for one of these heated, melt-up

rallies where the momentum keeps winning," Dickson added. "I

would not be surprised at all to be sitting here at the end of

the summer a good bit higher."

Tehran is studying a U.S. proposal to bring the war to a

halt, but has not been in contact with Washington for days,

according to Iranian media, which also said Iran is taking a

"stern" approach, given what it views as a history of U.S.

noncompliance and mutual distrust.

Simultaneously, Israel is continuing its strikes on Lebanon,

despite Tehran's warnings that the attacks are threatening to

derail the fragile truce.

The war has sent crude prices soaring, reviving worries over

inflation and giving rise to an increasing likelihood that the

U.S. Federal Reserve could hike interest rates by year-end.

Cleveland Fed President Beth Hammack said on Tuesday that such a

hike could become necessary if already-elevated inflation

pressures continue to mount.

On the economic front, a report from the Labor Department showed

an unexpected spike in job openings, driven by the volatile

professional and business services sector. Otherwise, hiring,

firing and quits all decreased, suggesting a slowdown in labor

market churn in the face of uncertainties related to strife in

the Middle East and inflationary effects.

Analysts look to the May employment report due on Friday,

which is expected to show the U.S. economy added 85,000 jobs

last month, a monthly deceleration of 26.1%. The unemployment

rate is forecast to stand pat at 4.3%.

According to preliminary data, the S&P 500 gained

10.07 points, or 0.13%, to end at 7,610.03 points, while the

Nasdaq Composite gained 8.78 points, or 0.03%, to

27,095.59. The Dow Jones Industrial Average rose 237.13

points, or 0.46%, to 51,316.01.

Hewlett Packard Enterprise ( HPE ) jumped after the AI server maker

pulled forward its long-term financial targets by two years.

In further evidence of AI buildout, Alphabet said it

was looking to raise $80 billion in equity offerings, including

an investment from Berkshire Hathaway, to fund a costly

expansion of its AI infrastructure. Its shares lost ground on

the day.

Marvell Technology's ( MRVL ) shares surged after Nvidia ( NVDA )

Chief Executive Officer Jensen Huang called the

chipmaker the next "trillion-dollar company" at the Computex

conference in Taipei. Nvidia ( NVDA ) invested $2 billion in Marvell ( MRVL ) in

March.

A drop in bitcoin hit cryptocurrency firms Coinbase

and Strategy Inc. ( MSTR )

Broadcom ( AVGO ) is expected to report quarterly results on

Wednesday.