WASHINGTON—At the White House on Sunday evening, as the phones started ringing nonstop and emails flooded in, President Trump took aim at the cause of the alarm: John Bolton, his former national security adviser.

Mr. Bolton’s recollection in his forthcoming book—that Mr. Trump had put a hold on Ukraine aid to press Kyiv to open an investigation of former Vice President Joe Biden—had just leaked. The information ran counter to a key Trump defense that he had held up the aid because of broad corruption concerns, and it turned…

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