WASHINGTON—Four federal prosecutors withdrew from the case against Roger Stone on Tuesday, with one resigning as an assistant U.S. attorney, as the Justice Department reversed itself and recommended less prison time for President Trump’s longtime confidant.

The Justice Department’s move to withdraw the recommendation it made on Monday to a U.S. judge and propose a more lenient one came hours after President Trump criticized in a tweet the original request that Mr. Stone spend more than seven years behind bars.

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