(Reuters) - U.S. stock index futures gained on Tuesday, recovering after a selloff in the previous session, as investors await fresh clues on the interest rate path from key inflation data and the third-quarter earnings season that starts later this week.

All three major indexes closed down around 1% on Monday, as a jump in Treasury yields, concerns about the impact of rising conflict in the Middle East and a repricing of U.S. rate expectation pressured equities.

At 5:35 a.m. ET, U.S. S&P 500 E-minis were up 20 points, or 0.35%, Nasdaq 100 E-minis were up 75.75 points, or 0.38%, Dow E-minis were up 70 points, or 0.17%

U.S. Treasury yields retreated slightly from Monday's highs, though the yield on the benchmark 10-year note remained above 4% as strong economic data last week prompted investors to trim bets on the scope of the Federal Reserve interest rate cuts over the rest of this year.

Traders have priced in a nearly 89% chance of a 25 basis point interest rate cut from the Fed at its November meeting. Bets on no rate change at the meeting also crept up slightly, according to CME FedWatch.

The S&P 500 is expected to report a 3.2% year-over-year earnings per share (EPS) rise in the third quarter, "with gains for six of its 11 sectors," said Sam Stovall, chief investment strategist at CFRA Research.

Fed Governor Adriana Kugler said earlier on Tuesday she supported further interest rate cuts if inflation continues to ease, as she expects.

Some Fed officials, including John Williams and Alberto Musalem, had said on Monday that it would be appropriate to reduce rates over time.

A number of other Fed officials are expected to speak later in the day, including Raphael Bostic, Susan Collins and Philip Jefferson.

International trade balance data for August is also due later on Tuesday.

Investors were also watching out for the impacts of category 4 Hurricane Milton on the markets.

Among single stocks, shares of Honeywell International rose 2.9% after a report that the company is planning to spin off its advanced materials business.

U.S.-listed shares of Chinese companies slid, tracking losses in domestic stocks, as optimism over China's stimulus measures waned due to the absence of more specific details.

Shares of Alibaba Group, JD.com and PDD Holdings slumped between 8.3% and 10.8%.

(Reporting by Lisa Mattackal in Bengaluru; Editing by Shinjini Ganguli)