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* Futures: Dow down 0.04%, S&P down 0.03%, Nasdaq up 0.04%

June 6 (Reuters) - The S&P 500 and the Dow futures were little changed on Thursday as investors awaited fresh data to gauge the U.S. labor market strength, while the Nasdaq futures inched higher as gains in AI-favorite Nvidia boosted optimism around the tech sector.

A tech rally on Wednesday drove the S&P 500 and the Nasdaq to all-time highs, as a string of weakening economic data boosted bets that the Federal Reserve could start easing policy sooner than previously expected.

Megacap tech stocks were the main driver of the rally, with the tech sector gaining nearly 2.6% as Treasury yields eased. Stocks including Meta Platforms, Microsoft and Apple were down between 0.04% and 0.3% in premarket trading.

However, chip maker Nvidia was up 1.0%, after crossing $3 trillion in market valuation in the previous session that saw it overtake Apple as the world's second most valuable company.

Gains in Nvidia and other AI-related players have been the primary driver of Wall Street's recent rally, with the chipmaker accounting for roughly a third of the S&P 500's over 12% year-to-date gains, even as investors have grappled with worries about higher-for-longer U.S. interest rates.

"The fact Nvidia is now worth more than Apple is striking ... there is a feeling that as long as Nvidia's share price is rising, investors are happy and everything is fine on the markets," said Russ Mould, investment director at AJ Bell.

On the macro front, May private payrolls data on Wednesday suggested an easing in labor market tightness, ahead of the crucial nonfarm payrolls report due Friday.

Traders now see a nearly 67% chance of a September rate reduction, according to the CME's FedWatch tool, and have priced in about two cuts this year, as per data from LSEG.

Forecasters polled by Reuters also expect two cuts, but there is a significant risk that the Fed would opt for only one or none at all.

Data on weekly jobless claims data and April's international trade figures are due later on Thursday.

At 5:54 a.m. ET, Dow e-minis were down 17 points, or 0.04%, S&P 500 e-minis were down 1.75 points, or 0.03%, and Nasdaq 100 e-minis were up 8.5 points, or 0.04%.

Among individual names, Lululemon Athletica leapt 7.1% after beating expectations for first-quarter profit and revenue on Wednesday, as its China-based business helped offset slowdowns in North America.

Meanwhile, Victoria's Secret lost 2.5% after posting lower first-quarter profit and revenue after markets closed Wednesday.

(Reporting by Lisa Mattackal in Bengaluru; Editing by Pooja Desai)