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* Futures down: Dow 0.30%, S&P 0.12%, Nasdaq 0.16%

April 2 (Reuters) - U.S. stock index futures dipped on Tuesday, hurt by sharp losses in shares of health insurers, while investors awaited more economic data and comments from Federal Reserve officials for hints on the timing of interest rate cuts.

Shares of UnitedHealth, CVS Health and Humana fell between 3.8% and 8.7% in premarket trading as the U.S. government's unchanged reimbursement rates for providers of Medicare Advantage health plans signaled that insurers' margins would likely remain under pressure next year.

The blue-chip Dow and the benchmark S&P 500 closed down on Monday after stronger-than-expected manufacturing data raised doubts over the Fed's three interest rate cuts that it had outlined in its forecast at the last policy meeting.

Data expected on Tuesday includes factory orders and job openings in February. However, the main focus is on Friday's U.S. non-farm payrolls data, which is expected to show job additions slowed in March although average earnings ticked higher compared to the previous month.

"Markets will be looking for a figure that is neither too hot as an overheated market might postpone rate cuts, or too cold as disappointing data would increase speculation of a hard economic landing," said Russ Mould, investment director at AJ Bell.

Traders are pricing in a 62% chance of the Fed cutting interest rates by 25 basis points in June, as well as see two more cuts in 2024, as per CMEGroup's FedWatch tool.

A host of Fed officials including New York Fed President John Williams, Cleveland Fed President Loretta Mester and San Francisco President Mary Daly are scheduled to speak later in the day.

At 5:53 a.m. ET, Dow e-minis were down 119 points, or 0.3%, S&P 500 e-minis were down 6.5 points, or 0.12%, and Nasdaq 100 e-minis were down 29.5 points, or 0.16%.

The subdued start to the new quarter comes on the heels of the S&P 500's strongest first quarter in five years and all the three major indexes hitting record highs, helped by optimism around artificial intelligence and expectations of easing monetary policy.

Among other stocks, Calvin Klein-parent PVH Corp's shares tumbled 23.4% after the retailer forecast an about 11% drop in first-quarter revenue. (Reporting by Sruthi Shankar in Bengaluru; Editing by Shinjini Ganguli)