Updates to afternoon trading

By Caroline Valetkevitch

NEW YORK, Aug 7 (Reuters) - The three major U.S. stock indexes fell on Thursday, with shares of Intel down after U.S. President Donald Trump demanded that the Intel CEO resign, while investors digested a report on the president's top pick for the Federal Reserve chair.

Bloomberg reported that Fed Governor Christopher Waller was Trump's top candidate for the U.S. central bank's chair post.

Trump has been critical of current Chair Jerome Powell for holding off on cutting borrowing costs. Many investors expect the Fed to cut interest rates in September.

Chipmaker Intel INTC.O was down 3.7% after Trump called for the immediate resignation of new Intel CEO Lip-Bu Tan, calling him "highly conflicted" due to his ties to Chinese firms.

Apple AAPL.O shares rose 3% after the latest tariff salvo from Trump largely exempted industry heavyweights from his threat to impose 100% levy on chips and semiconductors.

The U.S. president announced a tariff of about 100% on imports of semiconductors, but said it would not apply to companies that are manufacturing in the U.S. or have committed to do so.

Trump's higher tariffs on imports from dozens of countries kicked in on Thursday, raising the average U.S. import duty to its highest in a century.

"The market rally is beginning to look a little bit tired here. We ran up on earnings, and of course the market was basically ignoring a lot of the tariff news," said Peter Cardillo, chief market economist at Spartan Capital Securities in New York.

The Dow Jones Industrial Average .DJI fell 333.27 points, or 0.75%, to 43,859.85, the S&P 500 .SPX lost 28.61 points, or 0.45%, to 6,316.45 and the Nasdaq Composite .IXIC lost 50.62 points, or 0.24%, to 21,118.81.

Nvidia NVDA.O and Broadcom AVGO.O shares were down slightly.

Trump is also anticipated to announce his interim replacement for Fed Governor Adriana Kugler in the coming days amid expectations that the nominee would be a policy dove who will likely favor bringing interest rates lower.

Rate cut expectations remained largely the same after the day's data on the labor market.

Weekly initial jobless claims rose 7,000 to a seasonally adjusted 226,000, the highest level since the week ended July 5 and slightly above the 221,000 estimate of economists polled by Reuters, according to the data.

Market expectations for a September rate cut of at least 25 basis points from the Fed stood at 93.2%, down slightly from the 94.6% in the prior session and well above the 37.7% from a week ago, according to CME's FedWatch Tool.

In other decliners, shares of drugmaker Eli Lilly LLY.N dropped 14.3% after it reported data on its late-stage oral weight-loss drug. The drugmaker also raised its full-year profit forecast.

Declining issues outnumbered advancers by a 1.12-to-1 ratio on the NYSE. There were 206 new highs and 68 new lows on the NYSE.

On the Nasdaq, 1,705 stocks rose and 2,749 fell as declining issues outnumbered advancers by a 1.61-to-1 ratio.

(Additional reporting by Nikhil Sharma and Pranav Kashyap in Bengaluru; Editing by Maju Samuel and Aurora Ellis)

((caroline.valetkevitch@thomsonreuters.com))