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 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 to "reinvent the PC" for the AI era, Nvidia ( NVDA ) CEO Jensen Huang said. Microsoft 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 results on Wednesday. Broadcom 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 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.

(Reporting by Medha Singh in Bengaluru; Editing by Shinjini Ganguli)