(Reuters) -U.S. stock index futures were subdued on Tuesday as investors awaited the outcome of a second day of trade talks between the United States and China aimed at cooling a tariff dispute that has bruised global markets this year.

Investors are hoping for an improvement in ties after the relief sparked by a preliminary deal agreed in Geneva last month gave way to fresh doubts when Washington accused Beijing of blocking exports that are critical to sectors including autos, aerospace, semiconductors and defense.

White House economic adviser Kevin Hassett said on Monday the U.S. was likely to agree to lift export controls on some semiconductors in return for China speeding up the delivery of rare earths.

"The pause in tariff hostilities is a positive starting point as the U.S. seeks the restoration of rare earth mineral exports from China which would inevitably result in a mutual relaxation," Richard Hunter, head of markets at interactive investor, said in a morning note.

At 05:44 a.m. ET, Dow E-minis were down 35 points, or 0.08%, S&P 500 E-minis were up 2.75 points, or 0.05%. Nasdaq 100 E-minis were up 12.25 points, or 0.06%

U.S. equities rallied sharply in May, with investors boosting the S&P 500 index and the tech-heavy Nasdaq to their biggest monthly percentage gain since November 2023, helped by upbeat earnings reports and a softening of President Donald Trump's harsh trade stance.

The S&P 500 remains a little over 2% below all-time highs touched in February, while the Nasdaq is about 3% below its record peaks reached in December.

Investors are awaiting U.S. consumer prices data on Wednesday for clues on the Federal Reserve's rate trajectory.

While traders largely expect the Fed to keep interest rates unchanged next week, focus will be on any signs of pick-up in inflation as Trump's tariffs risk raising price pressures.

Traders see at least two 25-basis point cuts by year-end, with a 63% chance of the first cut in September, according to the CME FedWatch tool.

Shares of vaccine makers dipped in premarket trading. Health Secretary Robert F. Kennedy Jr. ousted all 17 members of a U.S. Centers for Disease Control and Prevention panel of vaccine experts and is in the process of replacing them, his department announced on Monday.

Shares of vaccine maker Moderna were down 0.5% while Pfizer inched down 0.1%.

(Reporting by Kanchana Chakravarty in Bengaluru; Editing by Devika Syamnath)