(Reuters) -U.S. stock index futures pointed to a higher open on Tuesday, as investors turned their focus to the start of the third-quarter earnings season later this week and key inflation data for clues on the Federal Reserve's rate path.

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 on oil prices, and a repricing of U.S. rate expectation pressured equities.

While the two-year Treasury yield retreated slightly from Monday's highs, 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 Fed's 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.

U.S. S&P 500 E-minis were up 19.75 points, or 0.34%, Nasdaq 100 E-minis were up 72.5 points, or 0.36%, and Dow E-minis were up 45 points, or 0.11%

"We did see strong sell off yesterday so it's not unnatural to see a slight bounce, particularly as there's a vacuum of fresh data today," said Fiona Cincotta, senior market analyst at City Index.

Traders will closely monitor consumer price index data, due this Thursday, for the next major clue on the path of interest rates.

"We do see an upside to Treasury yields in the very short term, it has the potential to pressure equities since they're trading at such high valuations," said Cameron Dawson, chief investment officer at NewEdge Wealth.

The CBOE Volatility index, Wall Street's "fear gauge," retreated from Monday's highs but was still trading around one-month high at 22.04.

Meanwhile, PepsiCo lost 0.5% in premarket trading after the packaged food giant posted a surprise drop in third-quarter revenue and cut its forecast for annual sales growth.

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.

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

Among single stocks, shares of Honeywell International rose 1.8% 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 6.3% and 8.1%.

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