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* Futures up: Dow 0.28%, S&P 0.23%, Nasdaq 0.29%

June 1 (Reuters) - U.S. stock index futures climbed on

Monday, starting June on a firm footing, as the latest AI push

from Nvidia ( NVDA ) and Microsoft ( MSFT ) lifted shares, even as uncertainty

over the Middle East war lingered.

Nvidia ( NVDA ) rose 1.6% in premarket trading after the

world's most valuable company unveiled a new chip that brings AI

capabilities to laptops and desktops, set for release this fall.

The chip is a result of a three-year partnership with

Microsoft ( MSFT ) to "reinvent the PC" for the AI era, Nvidia ( NVDA )

CEO Jensen Huang said. Microsoft ( MSFT ) shares gained 2.8%.

Other PC chipmakers dropped. AMD and Intel fell 3.4%

and 2.9%, respectively.

The broader mood was more somber and oil prices climbed

after the latest exchange of attacks between the U.S. and Iran

raised concerns over efforts to negotiate to end the

three-month-old war.

Wall Street's main indexes closed May at record highs,

lifted by hopes of an eventual end to the Middle East war and

blowout first-quarter earnings.

Investors now turn to Friday's jobs report ahead of Kevin

Warsh's debut policy meeting as the chairman of the U.S. Federal

Reserve this month, against a backdrop of rising inflation fears

linked to the Iran war.

Traders price in a near 70% chance of a one-quarter-point

rate hike before the end of the year.

At 05:18 a.m. ET, Dow E-minis were up 143 points, or

0.28%, and S&P 500 E-minis were up 17.5 points, or

0.23%. Nasdaq 100 E-minis were up 86.75 points, or

0.29%.

After AI server maker Dell posted a strong results

outlook last week, focus will shift to Broadcom ( AVGO ) results

on Wednesday. Broadcom ( AVGO ) is the second-largest U.S. chipmaker by

market value after Nvidia ( NVDA ).

Comments from a slew of Fed officials and a beige book

report will also be in focus this week before the central bank

enters its pre-meeting blackout period on Saturday.

In other company news, Cadence Design Systems ( CDNS ) rose

8.2% after launching an autonomous engineer for chip design,

powered by Nvidia ( NVDA ).

Micron advanced 5.3% to $1,022, topping the $1,000

mark for the first time. Its shares have soared nearly 90% in

May.