WASHINGTON—President Trump sought to use the powers of his office to push Ukraine to investigate Democratic rival Joe Biden, and White House officials acted to conceal evidence of the president’s actions, a whistleblower complaint alleges.

The whistleblower’s complaint, released Thursday, concerns a July phone call between Mr. Trump and President Volodymyr Zelensky of Ukraine. The controversy has become the biggest political danger to Mr. Trump’s presidency as it rallied House Democrats this week to launch impeachment proceedings.

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