U.S. stock index futures climbed Monday, starting June on a firm footing, as the latest AI push from Nvidia and Microsoft lifted shares, even as uncertainty over the Middle East war lingered.

Nvidia rose 1.6 percent in premarket trading after the company unveiled a new chip bringing AI capabilities to laptops and desktops, set for release this fall. The chip is the result of a three-year partnership with Microsoft to "reinvent the PC" for the AI era, Nvidia CEO Jensen Huang said. Microsoft shares gained 2.8 percent.

Other PC chipmakers dropped. AMD and Intel fell 3.4 percent and 2.9 percent, 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 peace negotiations.

Wall Street's main indexes closed May at record highs. Investors now turn to Friday's jobs report ahead of Kevin Warsh's debut policy meeting as Fed chairman this month, against a backdrop of rising inflation fears linked to the Iran war. Traders price in a near 70 percent chance of a rate hike by year-end.

At 05:18 a.m. ET, Dow E-minis were up 143 points, S&P 500 E-minis up 17.5 points, and Nasdaq 100 E-minis up 86.75 points.

Focus will shift to Broadcom results on Wednesday. In other company news, Cadence Design Systems rose 8.2 percent after launching an autonomous engineer for chip design powered by Nvidia. Micron advanced 5.3 percent to top the $1,000 mark for the first time.