June 16 (Reuters) - U.S. stock index futures were subdued on Tuesday as investors switched focus to the first interest rate decision under new Federal Reserve Chairman Kevin Warsh, while SpaceX extended its post-IPO run for a third day.

Tech stocks were a bright spot in premarket trading, with shares of SpaceX climbing 10%, putting the space and AI giant on course to overtake Amazon in market value and become the world's fifth-largest company.

Memory chip stocks also jumped, with Micron Technology, Western Digital and Seagate Technology rising between 2.9% and 4.8%.

The blue-chip Dow closed at a record high on Monday after U.S. President Donald Trump said a preliminary agreement to end the conflict had been signed by the U.S. and Iran, sending oil prices sharply lower and easing concerns about inflation.

Still, doubts swirled around the deal as shippers said it could take weeks for confidence to return after any reopening of the Strait of Hormuz.

The Fed is widely expected to hold interest rates at the 3.50-3.75% range at the end of its policy meeting on Wednesday, with investors closely watching Warsh's comments on inflation, unemployment and the economic outlook, potentially market-moving words of the world's most important central banker.

Inflation, in particular, seems stuck more than a percentage point above the Fed's 2% target, and Warsh's characterization about whether and when it is likely to fall will be a key first step in the evolution of monetary policy under his leadership.

Traders see a 42% chance of a 25-basis-point rate hike in December, as per CME Group's FedWatch tool, with rate cuts seen coming only after mid-2027.

The Bank of Japan raised interest rates to a 31-year high earlier on Tuesday, as it focused on taming price pressures from the energy shock caused by the Iran war.

At 5:58 a.m. ET, S&P 500 e-minis were down 6 points, or 0.08%. Nasdaq 100 e-minis were up 5.25 points, or 0.02%, and Dow e-minis added 20 points, or 0.04%.

The benchmark S&P 500 was also closing in on early June record highs after a slump driven by concerns about high valuations in the technology sector and the U.S.-Iran conflict.

Qualcomm rose 3.8% after the Information reported that the chipmaker was in talks to acquire AI chip startup Tenstorrent for $8 billion to $10 billion.

Shares of Dave & Buster's Entertainment fell 13.3% after the entertainment firm missed analysts' expectations for first-quarter earnings and revenue.