June 9 (Reuters) - U.S. stock index futures climbed on Tuesday, as chip stocks extended gains for a second day, while easing hostilities in the Middle East also aided sentiment.

Nasdaq futures led gains in early trading, with shares of chipmakers Nvidia, Broadcom and Micron Technology rising between 0.8% and 4.4% premarket, extending their rebound after Friday's sharp selloff.

Iran and Israel said on Monday that they had halted attacks on each other after an appeal from U.S. President Donald Trump, settling back into a tenuous ceasefire announced on April 8.

Oil prices fell more than 2%, erasing most of the previous session's gains, though caution lingered as diplomatic efforts have yet to yield a lasting peace agreement and the Strait of Hormuz remains shut. [O/R]

At 05:57 a.m. ET, Dow E-minis were up 120 points, or 0.24%, and S&P 500 E-minis were up 34.75 points, or 0.47%. Nasdaq 100 E-minis were up 238 points, or 0.81%.

Technology and AI stocks came under sharp selling pressure last week, after Broadcom's disappointing forecast fueled concerns about high valuations in the sector, particularly chipmakers that have rallied strongly this year.

A stronger-than-expected jobs report on Friday also added to concerns that the Federal Reserve will raise interest rates this year.

Consumer prices data for May, due on Wednesday, could offer fresh clues on how the rise in energy prices due to the Iran war is impacting inflation.

SpaceX's $1.75 trillion market debut on Friday could also prove to be a hurdle for U.S. stocks as investors worry about possible overexuberance among high-growth technology stocks. Elon Musk's SpaceX is aiming to raise $75 billion, the most ever for an IPO.

ChatGPT maker OpenAI said on Monday it had confidentially filed for a U.S. initial public offering, joining rival Anthropic in a push toward public markets.

Applied Digital rose 11.5% after it signed a 15-year lease with a U.S.-based hyperscaler at its Delta Forge 2 site, which is expected to generate about $5.2 billion in revenue over the period.Shares of cancer drug developer Nuvalent jumped 39% after GSK agreed to buy the company for $10.6 billion, in its largest deal in years, valuing Nuvalent at about $124 per share, a 40% premium to the stock's last closing price.

(Reporting by Joel Jose and Sruthi Shankar in Bengaluru; Editing by Shinjini Ganguli)